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add rush hour puzzle, sudoku puzzle and first try for jobs puzzle, they are... 

add rush hour puzzle, sudoku puzzle and first try for jobs puzzle, they are not completed MC missing
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%% Cell type:markdown id: tags:
# Rush Hour Puzzle
The [rush hour puzzle](https://en.wikipedia.org/wiki/Rush_Hour_(puzzle)) was invented in 1970 by Nob Yoshigahara. Even though the puzzle is one of the older puzzles, it is very interesting to model.
In this notebook we are going to look at one encoding for the rush hour board game in which cars are packed on a 6-by-6 grid and can either move horizontally or vertically. The goal is to move the red car to the exit.
In this particular instance we try to solve the [hardest puzzle of the original game Nr. 40](www.puzzles.com/products/RushHour/RHfromMarkRiedel/Jam.html?40).
Inspired by discussions with Neng-Fa Zhou at ICLP'14 in Vienna, we now have a new version of the B model for this puzzle.
The old version can still be found in the our [modelling examples](https://www3.hhu.de/stups/handbook/prob2/modelling_examples.html#rush-hour-puzzle)
Let us take a look at the B model of the Rush Hour Puzzle.
%% Cell type:code id: tags:
``` prob
::load
MACHINE RushHour
/* a more elegant encoding of the Rush Hour puzzle */
/* Michael Leuschel, July 2014 */
/* ProB finds solution in about 10.5 secs (turning invariant checking off) */
/* This version has been slightly adapted for TLC by adding the c:1..red guards:
it finds a solution in 3 seconds
(most of this time is spent replaying the counter ; the model checking seems less than a
second) */
SETS DIR = {h,v}
CONSTANTS sze, dir, red, dim, free_initial
PROPERTIES
sze = [2,2,2,2,2, 2,2,2,2, 3,3,3, 2] & /* the sizes of the cars */
dir = [v,v,v,v,v, h,h,h,h, v,v,h, h] & /* indicating whether the cars move vertically or horizontally */
red = size(sze) & /* the last car is the red one */
dim = 5 & /* the grid goes from 0..dim */
free_initial = {(0,3),(1,3), (0,5), (3,4),(4,0),(4,1),(5,5)}
DEFINITIONS
GOAL == (col(red) = 4); /* The target : move red car to the right */
ANIMATION_STR_JUSTIFY_RIGHT == TRUE;
ANIMATION_FUNCTION_DEFAULT == (0..dim)*(0..dim)*{-1};
ANIMATION_FUNCTION ==
{r,c,i| i:1..red & dir(i)=h & row(i)=r & c:col(i)..col(i)+sze(i)-1} \/
{r,c,i| i:1..red & dir(i)=v & col(i)=c & r:row(i)..row(i)+sze(i)-1} \/
free * {0}
VARIABLES free, row, col
INVARIANT
free <: (0..dim)*(0..dim) & /* the currently free blocks */
card(free) = card(free_initial) &
row : 1..red --> 0..dim & /* the row of each car */
col : 1..red --> 0..dim /* the column for each car */
INITIALISATION
free := free_initial
||
col := [(1),(2),(2),(3),(4), /* vertical 2-size cars */
(0),(1),(3),(4), /* horiz. 2-size cars */
(0),(5), /* vertical 3-size cars */
(0), /* horiz. 3-size cars */
(3)] /* red car */
||
row := [(1),(1),(4),(3),(0),
(5),(0),(5),(4),
(0),(1),
(3),
(2)] /* red car */
OPERATIONS
mv_down(c,F) = PRE c:1..red & c |-> v : dir & F = row(c)+sze(c)|->col(c) &
F : free THEN
free := free - {F} \/ {row(c)|->col(c)} ||
row(c) := row(c)+1
END;
mv_up(c,F) = PRE c:1..red & c |-> v : dir & F = row(c)-1|->col(c) &
F : free THEN
free := free - {F} \/ {row(c)+sze(c)-1|->col(c)} ||
row(c) := row(c)-1
END;
mv_right(c,F) = PRE c:1..red & c |-> h : dir & F = row(c)|->col(c)+sze(c) &
F : free THEN
free := free - {F} \/ {row(c)|->col(c)} ||
col(c) := col(c)+1
END;
mv_left(c,F) = PRE c:1..red & c |-> h : dir & F = row(c)|->col(c)-1 &
F : free THEN
free := free - {F} \/ {row(c)|->col(c)+sze(c)-1} ||
col(c) := col(c)-1
END
END
```
%% Output
Loaded machine: RushHour
%% Cell type:markdown id: tags:
## Finding a Solution
Since jupyter notebook does not
%% Cell type:code id: tags:
``` prob
:constants
```
%% Output
Machine constants set up using operation 0: $setup_constants()
%% Cell type:code id: tags:
``` prob
:init
```
%% Output
Machine initialised using operation 1: $initialise_machine()
%% Cell type:code id: tags:
``` prob
:help
```
%% Output
Enter a B expression or predicate to evaluate it. To load a B machine, enter its source code directly, or use `:load` to load an external machine file.
You can also use any of the following commands. For more help on a particular command, run `:help commandname`.
## Evaluation
* `:eval` - Evaluate a formula and display the result.
* `:solve` - Solve a predicate with the specified solver.
* `:table` - Display an expression as a table.
* `:type` - Display the static type of a formula.
* `:prettyprint` - Pretty-print a predicate.
* `:let` - Evaluate an expression and store it in a local variable.
* `:unlet` - Remove a local variable.
* `:assert` - Ensure that the predicate is true, and show an error otherwise.
## Animation
* `::load` - Load a B machine from the given source code.
* `:load` - Load a machine from a file.
* `:constants` - Set up the current machine's constants.
* `:init` - Initialise the current machine with the specified predicate
* `:exec` - Execute an operation.
* `:browse` - Show information about the current state.
* `:trace` - Display all states and executed operations in the current trace.
* `:goto` - Go to the state with the specified index in the current trace.
* `:find` - Try to find a state for which the given predicate is true (in addition to the machine's invariant).
## Visualisation
* `:show` - Show the machine's animation function visualisation for the current state.
* `:dot` - Execute and show a dot visualisation.
## Verification
* `:check` - Check the machine's properties, invariant, or assertions in the current state.
* `:modelcheck` - Run the ProB model checker on the current model.
## Other
* `::render` - Render some content with the specified MIME type.
* `:bsymb` - Load all bsymb.sty command definitions, so that they can be used in $\LaTeX$ formulas in Markdown cells.
* `:groovy` - Evaluate the given Groovy expression.
* `:help` - Display help for a specific command, or general help about the REPL.
* `:pref` - View or change the value of one or more preferences.
* `:stats` - Show statistics about the state space.
* `:time` - Execute the given command and measure how long it takes to execute.
* `:version` - Display version info about the ProB 2 Jupyter kernel, ProB 2, and the underlying ProB CLI.
Enter a B expression or predicate to evaluate it. To load a B machine, enter its source code directly, or use :load to load an external machine file.
You can also use any of the following commands. For more help on a particular command, run :help commandname.
Evaluation:
:eval - Evaluate a formula and display the result.
:solve - Solve a predicate with the specified solver.
:table - Display an expression as a table.
:type - Display the static type of a formula.
:prettyprint - Pretty-print a predicate.
:let - Evaluate an expression and store it in a local variable.
:unlet - Remove a local variable.
:assert - Ensure that the predicate is true, and show an error otherwise.
Animation:
::load - Load a B machine from the given source code.
:load - Load a machine from a file.
:constants - Set up the current machine's constants.
:init - Initialise the current machine with the specified predicate
:exec - Execute an operation.
:browse - Show information about the current state.
:trace - Display all states and executed operations in the current trace.
:goto - Go to the state with the specified index in the current trace.
:find - Try to find a state for which the given predicate is true (in addition to the machine's invariant).
Visualisation:
:show - Show the machine's animation function visualisation for the current state.
:dot - Execute and show a dot visualisation.
Verification:
:check - Check the machine's properties, invariant, or assertions in the current state.
:modelcheck - Run the ProB model checker on the current model.
Other:
::render - Render some content with the specified MIME type.
:bsymb - Load all bsymb.sty command definitions, so that they can be used in $\LaTeX$ formulas in Markdown cells.
:groovy - Evaluate the given Groovy expression.
:help - Display help for a specific command, or general help about the REPL.
:pref - View or change the value of one or more preferences.
:stats - Show statistics about the state space.
:time - Execute the given command and measure how long it takes to execute.
:version - Display version info about the ProB 2 Jupyter kernel, ProB 2, and the underlying ProB CLI.
%% Cell type:code id: tags:
``` prob
:modelcheck
```
%% Output
Model Checking complete. No error nodes found.
%% Cell type:code id: tags:
``` prob
```
Sudoku_Solved.ipynb 0 → 100644
+ 391
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View file @ 83dcdd35
%% Cell type:markdown id: tags:
# Sudoku Solving in Jupyter Notebook
Another very interesting [modelling example](https://www3.hhu.de/stups/handbook/prob2/modelling_examples.html#sudoku-solved-in-the-prob-repl) is the Sudoku Solved in the ProB REPL. Since jupyter notebook can do just as much, I wanted to replicate that example for jupyter notebook.
For this notebook you will need to understand how to interact with a machine, in this case the default empty machine, which is loaded at the beginning of each notebook.
I recommend you check out the ProB Jupyter Notebook Overview before you start with this session. Let us begin by defining the domain `DOM` for the numbers to be put inside the Sudoku:
%% Cell type:code id: tags:
``` prob
:let DOM 1..9
```
%% Output
$\{1,2,3,4,5,6,7,8,9\}$
{1,2,3,4,5,6,7,8,9}
%% Cell type:markdown id: tags:
And the group of indices `SUBSQ` which can be used to costruct 3x3 sub-squares:
%% Cell type:code id: tags:
``` prob
:let SUBSQ {{1,2,3},{4,5,6},{7,8,9}}
```
%% Output
$\{\{1,2,3\},\{4,5,6\},\{7,8,9\}\}$
{{1,2,3},{4,5,6},{7,8,9}}
%% Cell type:markdown id: tags:
Now we need to encode the sets of pairs in `Diff1` and `Diff2` of coordinates at which the values in a sudoku have to be different. (This is the case if they lie on the same column or row respectively.)
%% Cell type:code id: tags:
``` prob
:let Diff1 {x1,x2,y1,y2| x1:DOM & x2:DOM & y1:DOM & y2:DOM & x1<x2 & y1=y2}
```
%% Output
$\{(1\mapsto 2\mapsto 1\mapsto 1),(1\mapsto 2\mapsto 2\mapsto 2),(1\mapsto 2\mapsto 3\mapsto 3),(1\mapsto 2\mapsto 4\mapsto 4),(1\mapsto 2\mapsto 5\mapsto 5),(1\mapsto 2\mapsto 6\mapsto 6),(1\mapsto 2\mapsto 7\mapsto 7),(1\mapsto 2\mapsto 8\mapsto 8),(1\mapsto 2\mapsto 9\mapsto 9),(1\mapsto 3\mapsto 1\mapsto 1),(1\mapsto 3\mapsto 2\mapsto 2),(1\mapsto 3\mapsto 3\mapsto 3),(1\mapsto 3\mapsto 4\mapsto 4),(1\mapsto 3\mapsto 5\mapsto 5),(1\mapsto 3\mapsto 6\mapsto 6),(1\mapsto 3\mapsto 7\mapsto 7),(1\mapsto 3\mapsto 8\mapsto 8),(1\mapsto 3\mapsto 9\mapsto 9),(1\mapsto 4\mapsto 1\mapsto 1),(1\mapsto 4\mapsto 2\mapsto 2),(1\mapsto 4\mapsto 3\mapsto 3),(1\mapsto 4\mapsto 4\mapsto 4),(1\mapsto 4\mapsto 5\mapsto 5),(1\mapsto 4\mapsto 6\mapsto 6),(1\mapsto 4\mapsto 7\mapsto 7),(1\mapsto 4\mapsto 8\mapsto 8),(1\mapsto 4\mapsto 9\mapsto 9),(1\mapsto 5\mapsto 1\mapsto 1),(1\mapsto 5\mapsto 2\mapsto 2),(1\mapsto 5\mapsto 3\mapsto 3),(1\mapsto 5\mapsto 4\mapsto 4),(1\mapsto 5\mapsto 5\mapsto 5),(1\mapsto 5\mapsto 6\mapsto 6),(1\mapsto 5\mapsto 7\mapsto 7),(1\mapsto 5\mapsto 8\mapsto 8),(1\mapsto 5\mapsto 9\mapsto 9),(1\mapsto 6\mapsto 1\mapsto 1),(1\mapsto 6\mapsto 2\mapsto 2),(1\mapsto 6\mapsto 3\mapsto 3),(1\mapsto 6\mapsto 4\mapsto 4),(1\mapsto 6\mapsto 5\mapsto 5),(1\mapsto 6\mapsto 6\mapsto 6),(1\mapsto 6\mapsto 7\mapsto 7),(1\mapsto 6\mapsto 8\mapsto 8),(1\mapsto 6\mapsto 9\mapsto 9),(1\mapsto 7\mapsto 1\mapsto 1),(1\mapsto 7\mapsto 2\mapsto 2),(1\mapsto 7\mapsto 3\mapsto 3),(1\mapsto 7\mapsto 4\mapsto 4),(1\mapsto 7\mapsto 5\mapsto 5),(1\mapsto 7\mapsto 6\mapsto 6),(1\mapsto 7\mapsto 7\mapsto 7),(1\mapsto 7\mapsto 8\mapsto 8),(1\mapsto 7\mapsto 9\mapsto 9),(1\mapsto 8\mapsto 1\mapsto 1),(1\mapsto 8\mapsto 2\mapsto 2),(1\mapsto 8\mapsto 3\mapsto 3),(1\mapsto 8\mapsto 4\mapsto 4),(1\mapsto 8\mapsto 5\mapsto 5),(1\mapsto 8\mapsto 6\mapsto 6),(1\mapsto 8\mapsto 7\mapsto 7),(1\mapsto 8\mapsto 8\mapsto 8),(1\mapsto 8\mapsto 9\mapsto 9),(1\mapsto 9\mapsto 1\mapsto 1),(1\mapsto 9\mapsto 2\mapsto 2),(1\mapsto 9\mapsto 3\mapsto 3),(1\mapsto 9\mapsto 4\mapsto 4),(1\mapsto 9\mapsto 5\mapsto 5),(1\mapsto 9\mapsto 6\mapsto 6),(1\mapsto 9\mapsto 7\mapsto 7),(1\mapsto 9\mapsto 8\mapsto 8),(1\mapsto 9\mapsto 9\mapsto 9),(2\mapsto 3\mapsto 1\mapsto 1),(2\mapsto 3\mapsto 2\mapsto 2),(2\mapsto 3\mapsto 3\mapsto 3),(2\mapsto 3\mapsto 4\mapsto 4),(2\mapsto 3\mapsto 5\mapsto 5),(2\mapsto 3\mapsto 6\mapsto 6),(2\mapsto 3\mapsto 7\mapsto 7),(2\mapsto 3\mapsto 8\mapsto 8),(2\mapsto 3\mapsto 9\mapsto 9),(2\mapsto 4\mapsto 1\mapsto 1),(2\mapsto 4\mapsto 2\mapsto 2),(2\mapsto 4\mapsto 3\mapsto 3),(2\mapsto 4\mapsto 4\mapsto 4),(2\mapsto 4\mapsto 5\mapsto 5),(2\mapsto 4\mapsto 6\mapsto 6),(2\mapsto 4\mapsto 7\mapsto 7),(2\mapsto 4\mapsto 8\mapsto 8),(2\mapsto 4\mapsto 9\mapsto 9),(2\mapsto 5\mapsto 1\mapsto 1),(2\mapsto 5\mapsto 2\mapsto 2),(2\mapsto 5\mapsto 3\mapsto 3),(2\mapsto 5\mapsto 4\mapsto 4),(2\mapsto 5\mapsto 5\mapsto 5),(2\mapsto 5\mapsto 6\mapsto 6),(2\mapsto 5\mapsto 7\mapsto 7),(2\mapsto 5\mapsto 8\mapsto 8),(2\mapsto 5\mapsto 9\mapsto 9),(2\mapsto 6\mapsto 1\mapsto 1),(2\mapsto 6\mapsto 2\mapsto 2),(2\mapsto 6\mapsto 3\mapsto 3),(2\mapsto 6\mapsto 4\mapsto 4),(2\mapsto 6\mapsto 5\mapsto 5),(2\mapsto 6\mapsto 6\mapsto 6),(2\mapsto 6\mapsto 7\mapsto 7),(2\mapsto 6\mapsto 8\mapsto 8),(2\mapsto 6\mapsto 9\mapsto 9),(2\mapsto 7\mapsto 1\mapsto 1),(2\mapsto 7\mapsto 2\mapsto 2),(2\mapsto 7\mapsto 3\mapsto 3),(2\mapsto 7\mapsto 4\mapsto 4),(2\mapsto 7\mapsto 5\mapsto 5),(2\mapsto 7\mapsto 6\mapsto 6),(2\mapsto 7\mapsto 7\mapsto 7),(2\mapsto 7\mapsto 8\mapsto 8),(2\mapsto 7\mapsto 9\mapsto 9),(2\mapsto 8\mapsto 1\mapsto 1),(2\mapsto 8\mapsto 2\mapsto 2),(2\mapsto 8\mapsto 3\mapsto 3),(2\mapsto 8\mapsto 4\mapsto 4),(2\mapsto 8\mapsto 5\mapsto 5),(2\mapsto 8\mapsto 6\mapsto 6),(2\mapsto 8\mapsto 7\mapsto 7),(2\mapsto 8\mapsto 8\mapsto 8),(2\mapsto 8\mapsto 9\mapsto 9),(2\mapsto 9\mapsto 1\mapsto 1),(2\mapsto 9\mapsto 2\mapsto 2),(2\mapsto 9\mapsto 3\mapsto 3),(2\mapsto 9\mapsto 4\mapsto 4),(2\mapsto 9\mapsto 5\mapsto 5),(2\mapsto 9\mapsto 6\mapsto 6),(2\mapsto 9\mapsto 7\mapsto 7),(2\mapsto 9\mapsto 8\mapsto 8),(2\mapsto 9\mapsto 9\mapsto 9),(3\mapsto 4\mapsto 1\mapsto 1),(3\mapsto 4\mapsto 2\mapsto 2),(3\mapsto 4\mapsto 3\mapsto 3),(3\mapsto 4\mapsto 4\mapsto 4),(3\mapsto 4\mapsto 5\mapsto 5),(3\mapsto 4\mapsto 6\mapsto 6),(3\mapsto 4\mapsto 7\mapsto 7),(3\mapsto 4\mapsto 8\mapsto 8),(3\mapsto 4\mapsto 9\mapsto 9),(3\mapsto 5\mapsto 1\mapsto 1),(3\mapsto 5\mapsto 2\mapsto 2),(3\mapsto 5\mapsto 3\mapsto 3),(3\mapsto 5\mapsto 4\mapsto 4),(3\mapsto 5\mapsto 5\mapsto 5),(3\mapsto 5\mapsto 6\mapsto 6),(3\mapsto 5\mapsto 7\mapsto 7),(3\mapsto 5\mapsto 8\mapsto 8),(3\mapsto 5\mapsto 9\mapsto 9),(3\mapsto 6\mapsto 1\mapsto 1),(3\mapsto 6\mapsto 2\mapsto 2),(3\mapsto 6\mapsto 3\mapsto 3),(3\mapsto 6\mapsto 4\mapsto 4),(3\mapsto 6\mapsto 5\mapsto 5),(3\mapsto 6\mapsto 6\mapsto 6),(3\mapsto 6\mapsto 7\mapsto 7),(3\mapsto 6\mapsto 8\mapsto 8),(3\mapsto 6\mapsto 9\mapsto 9),(3\mapsto 7\mapsto 1\mapsto 1),(3\mapsto 7\mapsto 2\mapsto 2),(3\mapsto 7\mapsto 3\mapsto 3),(3\mapsto 7\mapsto 4\mapsto 4),(3\mapsto 7\mapsto 5\mapsto 5),(3\mapsto 7\mapsto 6\mapsto 6),(3\mapsto 7\mapsto 7\mapsto 7),(3\mapsto 7\mapsto 8\mapsto 8),(3\mapsto 7\mapsto 9\mapsto 9),(3\mapsto 8\mapsto 1\mapsto 1),(3\mapsto 8\mapsto 2\mapsto 2),(3\mapsto 8\mapsto 3\mapsto 3),(3\mapsto 8\mapsto 4\mapsto 4),(3\mapsto 8\mapsto 5\mapsto 5),(3\mapsto 8\mapsto 6\mapsto 6),(3\mapsto 8\mapsto 7\mapsto 7),(3\mapsto 8\mapsto 8\mapsto 8),(3\mapsto 8\mapsto 9\mapsto 9),(3\mapsto 9\mapsto 1\mapsto 1),(3\mapsto 9\mapsto 2\mapsto 2),(3\mapsto 9\mapsto 3\mapsto 3),(3\mapsto 9\mapsto 4\mapsto 4),(3\mapsto 9\mapsto 5\mapsto 5),(3\mapsto 9\mapsto 6\mapsto 6),(3\mapsto 9\mapsto 7\mapsto 7),(3\mapsto 9\mapsto 8\mapsto 8),(3\mapsto 9\mapsto 9\mapsto 9),(4\mapsto 5\mapsto 1\mapsto 1),(4\mapsto 5\mapsto 2\mapsto 2),(4\mapsto 5\mapsto 3\mapsto 3),(4\mapsto 5\mapsto 4\mapsto 4),(4\mapsto 5\mapsto 5\mapsto 5),(4\mapsto 5\mapsto 6\mapsto 6),(4\mapsto 5\mapsto 7\mapsto 7),(4\mapsto 5\mapsto 8\mapsto 8),(4\mapsto 5\mapsto 9\mapsto 9),(4\mapsto 6\mapsto 1\mapsto 1),(4\mapsto 6\mapsto 2\mapsto 2),(4\mapsto 6\mapsto 3\mapsto 3),(4\mapsto 6\mapsto 4\mapsto 4),(4\mapsto 6\mapsto 5\mapsto 5),(4\mapsto 6\mapsto 6\mapsto 6),(4\mapsto 6\mapsto 7\mapsto 7),(4\mapsto 6\mapsto 8\mapsto 8),(4\mapsto 6\mapsto 9\mapsto 9),(4\mapsto 7\mapsto 1\mapsto 1),(4\mapsto 7\mapsto 2\mapsto 2),(4\mapsto 7\mapsto 3\mapsto 3),(4\mapsto 7\mapsto 4\mapsto 4),(4\mapsto 7\mapsto 5\mapsto 5),(4\mapsto 7\mapsto 6\mapsto 6),(4\mapsto 7\mapsto 7\mapsto 7),(4\mapsto 7\mapsto 8\mapsto 8),(4\mapsto 7\mapsto 9\mapsto 9),(4\mapsto 8\mapsto 1\mapsto 1),(4\mapsto 8\mapsto 2\mapsto 2),(4\mapsto 8\mapsto 3\mapsto 3),(4\mapsto 8\mapsto 4\mapsto 4),(4\mapsto 8\mapsto 5\mapsto 5),(4\mapsto 8\mapsto 6\mapsto 6),(4\mapsto 8\mapsto 7\mapsto 7),(4\mapsto 8\mapsto 8\mapsto 8),(4\mapsto 8\mapsto 9\mapsto 9),(4\mapsto 9\mapsto 1\mapsto 1),(4\mapsto 9\mapsto 2\mapsto 2),(4\mapsto 9\mapsto 3\mapsto 3),(4\mapsto 9\mapsto 4\mapsto 4),(4\mapsto 9\mapsto 5\mapsto 5),(4\mapsto 9\mapsto 6\mapsto 6),(4\mapsto 9\mapsto 7\mapsto 7),(4\mapsto 9\mapsto 8\mapsto 8),(4\mapsto 9\mapsto 9\mapsto 9),(5\mapsto 6\mapsto 1\mapsto 1),(5\mapsto 6\mapsto 2\mapsto 2),(5\mapsto 6\mapsto 3\mapsto 3),(5\mapsto 6\mapsto 4\mapsto 4),(5\mapsto 6\mapsto 5\mapsto 5),(5\mapsto 6\mapsto 6\mapsto 6),(5\mapsto 6\mapsto 7\mapsto 7),(5\mapsto 6\mapsto 8\mapsto 8),(5\mapsto 6\mapsto 9\mapsto 9),(5\mapsto 7\mapsto 1\mapsto 1),(5\mapsto 7\mapsto 2\mapsto 2),(5\mapsto 7\mapsto 3\mapsto 3),(5\mapsto 7\mapsto 4\mapsto 4),(5\mapsto 7\mapsto 5\mapsto 5),(5\mapsto 7\mapsto 6\mapsto 6),(5\mapsto 7\mapsto 7\mapsto 7),(5\mapsto 7\mapsto 8\mapsto 8),(5\mapsto 7\mapsto 9\mapsto 9),(5\mapsto 8\mapsto 1\mapsto 1),(5\mapsto 8\mapsto 2\mapsto 2),(5\mapsto 8\mapsto 3\mapsto 3),(5\mapsto 8\mapsto 4\mapsto 4),(5\mapsto 8\mapsto 5\mapsto 5),(5\mapsto 8\mapsto 6\mapsto 6),(5\mapsto 8\mapsto 7\mapsto 7),(5\mapsto 8\mapsto 8\mapsto 8),(5\mapsto 8\mapsto 9\mapsto 9),(5\mapsto 9\mapsto 1\mapsto 1),(5\mapsto 9\mapsto 2\mapsto 2),(5\mapsto 9\mapsto 3\mapsto 3),(5\mapsto 9\mapsto 4\mapsto 4),(5\mapsto 9\mapsto 5\mapsto 5),(5\mapsto 9\mapsto 6\mapsto 6),(5\mapsto 9\mapsto 7\mapsto 7),(5\mapsto 9\mapsto 8\mapsto 8),(5\mapsto 9\mapsto 9\mapsto 9),(6\mapsto 7\mapsto 1\mapsto 1),(6\mapsto 7\mapsto 2\mapsto 2),(6\mapsto 7\mapsto 3\mapsto 3),(6\mapsto 7\mapsto 4\mapsto 4),(6\mapsto 7\mapsto 5\mapsto 5),(6\mapsto 7\mapsto 6\mapsto 6),(6\mapsto 7\mapsto 7\mapsto 7),(6\mapsto 7\mapsto 8\mapsto 8),(6\mapsto 7\mapsto 9\mapsto 9),(6\mapsto 8\mapsto 1\mapsto 1),(6\mapsto 8\mapsto 2\mapsto 2),(6\mapsto 8\mapsto 3\mapsto 3),(6\mapsto 8\mapsto 4\mapsto 4),(6\mapsto 8\mapsto 5\mapsto 5),(6\mapsto 8\mapsto 6\mapsto 6),(6\mapsto 8\mapsto 7\mapsto 7),(6\mapsto 8\mapsto 8\mapsto 8),(6\mapsto 8\mapsto 9\mapsto 9),(6\mapsto 9\mapsto 1\mapsto 1),(6\mapsto 9\mapsto 2\mapsto 2),(6\mapsto 9\mapsto 3\mapsto 3),(6\mapsto 9\mapsto 4\mapsto 4),(6\mapsto 9\mapsto 5\mapsto 5),(6\mapsto 9\mapsto 6\mapsto 6),(6\mapsto 9\mapsto 7\mapsto 7),(6\mapsto 9\mapsto 8\mapsto 8),(6\mapsto 9\mapsto 9\mapsto 9),(7\mapsto 8\mapsto 1\mapsto 1),(7\mapsto 8\mapsto 2\mapsto 2),(7\mapsto 8\mapsto 3\mapsto 3),(7\mapsto 8\mapsto 4\mapsto 4),(7\mapsto 8\mapsto 5\mapsto 5),(7\mapsto 8\mapsto 6\mapsto 6),(7\mapsto 8\mapsto 7\mapsto 7),(7\mapsto 8\mapsto 8\mapsto 8),(7\mapsto 8\mapsto 9\mapsto 9),(7\mapsto 9\mapsto 1\mapsto 1),(7\mapsto 9\mapsto 2\mapsto 2),(7\mapsto 9\mapsto 3\mapsto 3),(7\mapsto 9\mapsto 4\mapsto 4),(7\mapsto 9\mapsto 5\mapsto 5),(7\mapsto 9\mapsto 6\mapsto 6),(7\mapsto 9\mapsto 7\mapsto 7),(7\mapsto 9\mapsto 8\mapsto 8),(7\mapsto 9\mapsto 9\mapsto 9),(8\mapsto 9\mapsto 1\mapsto 1),(8\mapsto 9\mapsto 2\mapsto 2),(8\mapsto 9\mapsto 3\mapsto 3),(8\mapsto 9\mapsto 4\mapsto 4),(8\mapsto 9\mapsto 5\mapsto 5),(8\mapsto 9\mapsto 6\mapsto 6),(8\mapsto 9\mapsto 7\mapsto 7),(8\mapsto 9\mapsto 8\mapsto 8),(8\mapsto 9\mapsto 9\mapsto 9)\}$
{(1↦2↦1↦1),(1↦2↦2↦2),(1↦2↦3↦3),(1↦2↦4↦4),(1↦2↦5↦5),(1↦2↦6↦6),(1↦2↦7↦7),(1↦2↦8↦8),(1↦2↦9↦9),(1↦3↦1↦1),(1↦3↦2↦2),(1↦3↦3↦3),(1↦3↦4↦4),(1↦3↦5↦5),(1↦3↦6↦6),(1↦3↦7↦7),(1↦3↦8↦8),(1↦3↦9↦9),(1↦4↦1↦1),(1↦4↦2↦2),(1↦4↦3↦3),(1↦4↦4↦4),(1↦4↦5↦5),(1↦4↦6↦6),(1↦4↦7↦7),(1↦4↦8↦8),(1↦4↦9↦9),(1↦5↦1↦1),(1↦5↦2↦2),(1↦5↦3↦3),(1↦5↦4↦4),(1↦5↦5↦5),(1↦5↦6↦6),(1↦5↦7↦7),(1↦5↦8↦8),(1↦5↦9↦9),(1↦6↦1↦1),(1↦6↦2↦2),(1↦6↦3↦3),(1↦6↦4↦4),(1↦6↦5↦5),(1↦6↦6↦6),(1↦6↦7↦7),(1↦6↦8↦8),(1↦6↦9↦9),(1↦7↦1↦1),(1↦7↦2↦2),(1↦7↦3↦3),(1↦7↦4↦4),(1↦7↦5↦5),(1↦7↦6↦6),(1↦7↦7↦7),(1↦7↦8↦8),(1↦7↦9↦9),(1↦8↦1↦1),(1↦8↦2↦2),(1↦8↦3↦3),(1↦8↦4↦4),(1↦8↦5↦5),(1↦8↦6↦6),(1↦8↦7↦7),(1↦8↦8↦8),(1↦8↦9↦9),(1↦9↦1↦1),(1↦9↦2↦2),(1↦9↦3↦3),(1↦9↦4↦4),(1↦9↦5↦5),(1↦9↦6↦6),(1↦9↦7↦7),(1↦9↦8↦8),(1↦9↦9↦9),(2↦3↦1↦1),(2↦3↦2↦2),(2↦3↦3↦3),(2↦3↦4↦4),(2↦3↦5↦5),(2↦3↦6↦6),(2↦3↦7↦7),(2↦3↦8↦8),(2↦3↦9↦9),(2↦4↦1↦1),(2↦4↦2↦2),(2↦4↦3↦3),(2↦4↦4↦4),(2↦4↦5↦5),(2↦4↦6↦6),(2↦4↦7↦7),(2↦4↦8↦8),(2↦4↦9↦9),(2↦5↦1↦1),(2↦5↦2↦2),(2↦5↦3↦3),(2↦5↦4↦4),(2↦5↦5↦5),(2↦5↦6↦6),(2↦5↦7↦7),(2↦5↦8↦8),(2↦5↦9↦9),(2↦6↦1↦1),(2↦6↦2↦2),(2↦6↦3↦3),(2↦6↦4↦4),(2↦6↦5↦5),(2↦6↦6↦6),(2↦6↦7↦7),(2↦6↦8↦8),(2↦6↦9↦9),(2↦7↦1↦1),(2↦7↦2↦2),(2↦7↦3↦3),(2↦7↦4↦4),(2↦7↦5↦5),(2↦7↦6↦6),(2↦7↦7↦7),(2↦7↦8↦8),(2↦7↦9↦9),(2↦8↦1↦1),(2↦8↦2↦2),(2↦8↦3↦3),(2↦8↦4↦4),(2↦8↦5↦5),(2↦8↦6↦6),(2↦8↦7↦7),(2↦8↦8↦8),(2↦8↦9↦9),(2↦9↦1↦1),(2↦9↦2↦2),(2↦9↦3↦3),(2↦9↦4↦4),(2↦9↦5↦5),(2↦9↦6↦6),(2↦9↦7↦7),(2↦9↦8↦8),(2↦9↦9↦9),(3↦4↦1↦1),(3↦4↦2↦2),(3↦4↦3↦3),(3↦4↦4↦4),(3↦4↦5↦5),(3↦4↦6↦6),(3↦4↦7↦7),(3↦4↦8↦8),(3↦4↦9↦9),(3↦5↦1↦1),(3↦5↦2↦2),(3↦5↦3↦3),(3↦5↦4↦4),(3↦5↦5↦5),(3↦5↦6↦6),(3↦5↦7↦7),(3↦5↦8↦8),(3↦5↦9↦9),(3↦6↦1↦1),(3↦6↦2↦2),(3↦6↦3↦3),(3↦6↦4↦4),(3↦6↦5↦5),(3↦6↦6↦6),(3↦6↦7↦7),(3↦6↦8↦8),(3↦6↦9↦9),(3↦7↦1↦1),(3↦7↦2↦2),(3↦7↦3↦3),(3↦7↦4↦4),(3↦7↦5↦5),(3↦7↦6↦6),(3↦7↦7↦7),(3↦7↦8↦8),(3↦7↦9↦9),(3↦8↦1↦1),(3↦8↦2↦2),(3↦8↦3↦3),(3↦8↦4↦4),(3↦8↦5↦5),(3↦8↦6↦6),(3↦8↦7↦7),(3↦8↦8↦8),(3↦8↦9↦9),(3↦9↦1↦1),(3↦9↦2↦2),(3↦9↦3↦3),(3↦9↦4↦4),(3↦9↦5↦5),(3↦9↦6↦6),(3↦9↦7↦7),(3↦9↦8↦8),(3↦9↦9↦9),(4↦5↦1↦1),(4↦5↦2↦2),(4↦5↦3↦3),(4↦5↦4↦4),(4↦5↦5↦5),(4↦5↦6↦6),(4↦5↦7↦7),(4↦5↦8↦8),(4↦5↦9↦9),(4↦6↦1↦1),(4↦6↦2↦2),(4↦6↦3↦3),(4↦6↦4↦4),(4↦6↦5↦5),(4↦6↦6↦6),(4↦6↦7↦7),(4↦6↦8↦8),(4↦6↦9↦9),(4↦7↦1↦1),(4↦7↦2↦2),(4↦7↦3↦3),(4↦7↦4↦4),(4↦7↦5↦5),(4↦7↦6↦6),(4↦7↦7↦7),(4↦7↦8↦8),(4↦7↦9↦9),(4↦8↦1↦1),(4↦8↦2↦2),(4↦8↦3↦3),(4↦8↦4↦4),(4↦8↦5↦5),(4↦8↦6↦6),(4↦8↦7↦7),(4↦8↦8↦8),(4↦8↦9↦9),(4↦9↦1↦1),(4↦9↦2↦2),(4↦9↦3↦3),(4↦9↦4↦4),(4↦9↦5↦5),(4↦9↦6↦6),(4↦9↦7↦7),(4↦9↦8↦8),(4↦9↦9↦9),(5↦6↦1↦1),(5↦6↦2↦2),(5↦6↦3↦3),(5↦6↦4↦4),(5↦6↦5↦5),(5↦6↦6↦6),(5↦6↦7↦7),(5↦6↦8↦8),(5↦6↦9↦9),(5↦7↦1↦1),(5↦7↦2↦2),(5↦7↦3↦3),(5↦7↦4↦4),(5↦7↦5↦5),(5↦7↦6↦6),(5↦7↦7↦7),(5↦7↦8↦8),(5↦7↦9↦9),(5↦8↦1↦1),(5↦8↦2↦2),(5↦8↦3↦3),(5↦8↦4↦4),(5↦8↦5↦5),(5↦8↦6↦6),(5↦8↦7↦7),(5↦8↦8↦8),(5↦8↦9↦9),(5↦9↦1↦1),(5↦9↦2↦2),(5↦9↦3↦3),(5↦9↦4↦4),(5↦9↦5↦5),(5↦9↦6↦6),(5↦9↦7↦7),(5↦9↦8↦8),(5↦9↦9↦9),(6↦7↦1↦1),(6↦7↦2↦2),(6↦7↦3↦3),(6↦7↦4↦4),(6↦7↦5↦5),(6↦7↦6↦6),(6↦7↦7↦7),(6↦7↦8↦8),(6↦7↦9↦9),(6↦8↦1↦1),(6↦8↦2↦2),(6↦8↦3↦3),(6↦8↦4↦4),(6↦8↦5↦5),(6↦8↦6↦6),(6↦8↦7↦7),(6↦8↦8↦8),(6↦8↦9↦9),(6↦9↦1↦1),(6↦9↦2↦2),(6↦9↦3↦3),(6↦9↦4↦4),(6↦9↦5↦5),(6↦9↦6↦6),(6↦9↦7↦7),(6↦9↦8↦8),(6↦9↦9↦9),(7↦8↦1↦1),(7↦8↦2↦2),(7↦8↦3↦3),(7↦8↦4↦4),(7↦8↦5↦5),(7↦8↦6↦6),(7↦8↦7↦7),(7↦8↦8↦8),(7↦8↦9↦9),(7↦9↦1↦1),(7↦9↦2↦2),(7↦9↦3↦3),(7↦9↦4↦4),(7↦9↦5↦5),(7↦9↦6↦6),(7↦9↦7↦7),(7↦9↦8↦8),(7↦9↦9↦9),(8↦9↦1↦1),(8↦9↦2↦2),(8↦9↦3↦3),(8↦9↦4↦4),(8↦9↦5↦5),(8↦9↦6↦6),(8↦9↦7↦7),(8↦9↦8↦8),(8↦9↦9↦9)}
%% Cell type:code id: tags:
``` prob
:let Diff2 {x1,x2,y1,y2| x1:DOM & x2:DOM & y1:DOM & y2:DOM & x1=x2 & y1<y2}
```
%% Output
$\{(1\mapsto 1\mapsto 1\mapsto 2),(1\mapsto 1\mapsto 1\mapsto 3),(1\mapsto 1\mapsto 1\mapsto 4),(1\mapsto 1\mapsto 1\mapsto 5),(1\mapsto 1\mapsto 1\mapsto 6),(1\mapsto 1\mapsto 1\mapsto 7),(1\mapsto 1\mapsto 1\mapsto 8),(1\mapsto 1\mapsto 1\mapsto 9),(1\mapsto 1\mapsto 2\mapsto 3),(1\mapsto 1\mapsto 2\mapsto 4),(1\mapsto 1\mapsto 2\mapsto 5),(1\mapsto 1\mapsto 2\mapsto 6),(1\mapsto 1\mapsto 2\mapsto 7),(1\mapsto 1\mapsto 2\mapsto 8),(1\mapsto 1\mapsto 2\mapsto 9),(1\mapsto 1\mapsto 3\mapsto 4),(1\mapsto 1\mapsto 3\mapsto 5),(1\mapsto 1\mapsto 3\mapsto 6),(1\mapsto 1\mapsto 3\mapsto 7),(1\mapsto 1\mapsto 3\mapsto 8),(1\mapsto 1\mapsto 3\mapsto 9),(1\mapsto 1\mapsto 4\mapsto 5),(1\mapsto 1\mapsto 4\mapsto 6),(1\mapsto 1\mapsto 4\mapsto 7),(1\mapsto 1\mapsto 4\mapsto 8),(1\mapsto 1\mapsto 4\mapsto 9),(1\mapsto 1\mapsto 5\mapsto 6),(1\mapsto 1\mapsto 5\mapsto 7),(1\mapsto 1\mapsto 5\mapsto 8),(1\mapsto 1\mapsto 5\mapsto 9),(1\mapsto 1\mapsto 6\mapsto 7),(1\mapsto 1\mapsto 6\mapsto 8),(1\mapsto 1\mapsto 6\mapsto 9),(1\mapsto 1\mapsto 7\mapsto 8),(1\mapsto 1\mapsto 7\mapsto 9),(1\mapsto 1\mapsto 8\mapsto 9),(2\mapsto 2\mapsto 1\mapsto 2),(2\mapsto 2\mapsto 1\mapsto 3),(2\mapsto 2\mapsto 1\mapsto 4),(2\mapsto 2\mapsto 1\mapsto 5),(2\mapsto 2\mapsto 1\mapsto 6),(2\mapsto 2\mapsto 1\mapsto 7),(2\mapsto 2\mapsto 1\mapsto 8),(2\mapsto 2\mapsto 1\mapsto 9),(2\mapsto 2\mapsto 2\mapsto 3),(2\mapsto 2\mapsto 2\mapsto 4),(2\mapsto 2\mapsto 2\mapsto 5),(2\mapsto 2\mapsto 2\mapsto 6),(2\mapsto 2\mapsto 2\mapsto 7),(2\mapsto 2\mapsto 2\mapsto 8),(2\mapsto 2\mapsto 2\mapsto 9),(2\mapsto 2\mapsto 3\mapsto 4),(2\mapsto 2\mapsto 3\mapsto 5),(2\mapsto 2\mapsto 3\mapsto 6),(2\mapsto 2\mapsto 3\mapsto 7),(2\mapsto 2\mapsto 3\mapsto 8),(2\mapsto 2\mapsto 3\mapsto 9),(2\mapsto 2\mapsto 4\mapsto 5),(2\mapsto 2\mapsto 4\mapsto 6),(2\mapsto 2\mapsto 4\mapsto 7),(2\mapsto 2\mapsto 4\mapsto 8),(2\mapsto 2\mapsto 4\mapsto 9),(2\mapsto 2\mapsto 5\mapsto 6),(2\mapsto 2\mapsto 5\mapsto 7),(2\mapsto 2\mapsto 5\mapsto 8),(2\mapsto 2\mapsto 5\mapsto 9),(2\mapsto 2\mapsto 6\mapsto 7),(2\mapsto 2\mapsto 6\mapsto 8),(2\mapsto 2\mapsto 6\mapsto 9),(2\mapsto 2\mapsto 7\mapsto 8),(2\mapsto 2\mapsto 7\mapsto 9),(2\mapsto 2\mapsto 8\mapsto 9),(3\mapsto 3\mapsto 1\mapsto 2),(3\mapsto 3\mapsto 1\mapsto 3),(3\mapsto 3\mapsto 1\mapsto 4),(3\mapsto 3\mapsto 1\mapsto 5),(3\mapsto 3\mapsto 1\mapsto 6),(3\mapsto 3\mapsto 1\mapsto 7),(3\mapsto 3\mapsto 1\mapsto 8),(3\mapsto 3\mapsto 1\mapsto 9),(3\mapsto 3\mapsto 2\mapsto 3),(3\mapsto 3\mapsto 2\mapsto 4),(3\mapsto 3\mapsto 2\mapsto 5),(3\mapsto 3\mapsto 2\mapsto 6),(3\mapsto 3\mapsto 2\mapsto 7),(3\mapsto 3\mapsto 2\mapsto 8),(3\mapsto 3\mapsto 2\mapsto 9),(3\mapsto 3\mapsto 3\mapsto 4),(3\mapsto 3\mapsto 3\mapsto 5),(3\mapsto 3\mapsto 3\mapsto 6),(3\mapsto 3\mapsto 3\mapsto 7),(3\mapsto 3\mapsto 3\mapsto 8),(3\mapsto 3\mapsto 3\mapsto 9),(3\mapsto 3\mapsto 4\mapsto 5),(3\mapsto 3\mapsto 4\mapsto 6),(3\mapsto 3\mapsto 4\mapsto 7),(3\mapsto 3\mapsto 4\mapsto 8),(3\mapsto 3\mapsto 4\mapsto 9),(3\mapsto 3\mapsto 5\mapsto 6),(3\mapsto 3\mapsto 5\mapsto 7),(3\mapsto 3\mapsto 5\mapsto 8),(3\mapsto 3\mapsto 5\mapsto 9),(3\mapsto 3\mapsto 6\mapsto 7),(3\mapsto 3\mapsto 6\mapsto 8),(3\mapsto 3\mapsto 6\mapsto 9),(3\mapsto 3\mapsto 7\mapsto 8),(3\mapsto 3\mapsto 7\mapsto 9),(3\mapsto 3\mapsto 8\mapsto 9),(4\mapsto 4\mapsto 1\mapsto 2),(4\mapsto 4\mapsto 1\mapsto 3),(4\mapsto 4\mapsto 1\mapsto 4),(4\mapsto 4\mapsto 1\mapsto 5),(4\mapsto 4\mapsto 1\mapsto 6),(4\mapsto 4\mapsto 1\mapsto 7),(4\mapsto 4\mapsto 1\mapsto 8),(4\mapsto 4\mapsto 1\mapsto 9),(4\mapsto 4\mapsto 2\mapsto 3),(4\mapsto 4\mapsto 2\mapsto 4),(4\mapsto 4\mapsto 2\mapsto 5),(4\mapsto 4\mapsto 2\mapsto 6),(4\mapsto 4\mapsto 2\mapsto 7),(4\mapsto 4\mapsto 2\mapsto 8),(4\mapsto 4\mapsto 2\mapsto 9),(4\mapsto 4\mapsto 3\mapsto 4),(4\mapsto 4\mapsto 3\mapsto 5),(4\mapsto 4\mapsto 3\mapsto 6),(4\mapsto 4\mapsto 3\mapsto 7),(4\mapsto 4\mapsto 3\mapsto 8),(4\mapsto 4\mapsto 3\mapsto 9),(4\mapsto 4\mapsto 4\mapsto 5),(4\mapsto 4\mapsto 4\mapsto 6),(4\mapsto 4\mapsto 4\mapsto 7),(4\mapsto 4\mapsto 4\mapsto 8),(4\mapsto 4\mapsto 4\mapsto 9),(4\mapsto 4\mapsto 5\mapsto 6),(4\mapsto 4\mapsto 5\mapsto 7),(4\mapsto 4\mapsto 5\mapsto 8),(4\mapsto 4\mapsto 5\mapsto 9),(4\mapsto 4\mapsto 6\mapsto 7),(4\mapsto 4\mapsto 6\mapsto 8),(4\mapsto 4\mapsto 6\mapsto 9),(4\mapsto 4\mapsto 7\mapsto 8),(4\mapsto 4\mapsto 7\mapsto 9),(4\mapsto 4\mapsto 8\mapsto 9),(5\mapsto 5\mapsto 1\mapsto 2),(5\mapsto 5\mapsto 1\mapsto 3),(5\mapsto 5\mapsto 1\mapsto 4),(5\mapsto 5\mapsto 1\mapsto 5),(5\mapsto 5\mapsto 1\mapsto 6),(5\mapsto 5\mapsto 1\mapsto 7),(5\mapsto 5\mapsto 1\mapsto 8),(5\mapsto 5\mapsto 1\mapsto 9),(5\mapsto 5\mapsto 2\mapsto 3),(5\mapsto 5\mapsto 2\mapsto 4),(5\mapsto 5\mapsto 2\mapsto 5),(5\mapsto 5\mapsto 2\mapsto 6),(5\mapsto 5\mapsto 2\mapsto 7),(5\mapsto 5\mapsto 2\mapsto 8),(5\mapsto 5\mapsto 2\mapsto 9),(5\mapsto 5\mapsto 3\mapsto 4),(5\mapsto 5\mapsto 3\mapsto 5),(5\mapsto 5\mapsto 3\mapsto 6),(5\mapsto 5\mapsto 3\mapsto 7),(5\mapsto 5\mapsto 3\mapsto 8),(5\mapsto 5\mapsto 3\mapsto 9),(5\mapsto 5\mapsto 4\mapsto 5),(5\mapsto 5\mapsto 4\mapsto 6),(5\mapsto 5\mapsto 4\mapsto 7),(5\mapsto 5\mapsto 4\mapsto 8),(5\mapsto 5\mapsto 4\mapsto 9),(5\mapsto 5\mapsto 5\mapsto 6),(5\mapsto 5\mapsto 5\mapsto 7),(5\mapsto 5\mapsto 5\mapsto 8),(5\mapsto 5\mapsto 5\mapsto 9),(5\mapsto 5\mapsto 6\mapsto 7),(5\mapsto 5\mapsto 6\mapsto 8),(5\mapsto 5\mapsto 6\mapsto 9),(5\mapsto 5\mapsto 7\mapsto 8),(5\mapsto 5\mapsto 7\mapsto 9),(5\mapsto 5\mapsto 8\mapsto 9),(6\mapsto 6\mapsto 1\mapsto 2),(6\mapsto 6\mapsto 1\mapsto 3),(6\mapsto 6\mapsto 1\mapsto 4),(6\mapsto 6\mapsto 1\mapsto 5),(6\mapsto 6\mapsto 1\mapsto 6),(6\mapsto 6\mapsto 1\mapsto 7),(6\mapsto 6\mapsto 1\mapsto 8),(6\mapsto 6\mapsto 1\mapsto 9),(6\mapsto 6\mapsto 2\mapsto 3),(6\mapsto 6\mapsto 2\mapsto 4),(6\mapsto 6\mapsto 2\mapsto 5),(6\mapsto 6\mapsto 2\mapsto 6),(6\mapsto 6\mapsto 2\mapsto 7),(6\mapsto 6\mapsto 2\mapsto 8),(6\mapsto 6\mapsto 2\mapsto 9),(6\mapsto 6\mapsto 3\mapsto 4),(6\mapsto 6\mapsto 3\mapsto 5),(6\mapsto 6\mapsto 3\mapsto 6),(6\mapsto 6\mapsto 3\mapsto 7),(6\mapsto 6\mapsto 3\mapsto 8),(6\mapsto 6\mapsto 3\mapsto 9),(6\mapsto 6\mapsto 4\mapsto 5),(6\mapsto 6\mapsto 4\mapsto 6),(6\mapsto 6\mapsto 4\mapsto 7),(6\mapsto 6\mapsto 4\mapsto 8),(6\mapsto 6\mapsto 4\mapsto 9),(6\mapsto 6\mapsto 5\mapsto 6),(6\mapsto 6\mapsto 5\mapsto 7),(6\mapsto 6\mapsto 5\mapsto 8),(6\mapsto 6\mapsto 5\mapsto 9),(6\mapsto 6\mapsto 6\mapsto 7),(6\mapsto 6\mapsto 6\mapsto 8),(6\mapsto 6\mapsto 6\mapsto 9),(6\mapsto 6\mapsto 7\mapsto 8),(6\mapsto 6\mapsto 7\mapsto 9),(6\mapsto 6\mapsto 8\mapsto 9),(7\mapsto 7\mapsto 1\mapsto 2),(7\mapsto 7\mapsto 1\mapsto 3),(7\mapsto 7\mapsto 1\mapsto 4),(7\mapsto 7\mapsto 1\mapsto 5),(7\mapsto 7\mapsto 1\mapsto 6),(7\mapsto 7\mapsto 1\mapsto 7),(7\mapsto 7\mapsto 1\mapsto 8),(7\mapsto 7\mapsto 1\mapsto 9),(7\mapsto 7\mapsto 2\mapsto 3),(7\mapsto 7\mapsto 2\mapsto 4),(7\mapsto 7\mapsto 2\mapsto 5),(7\mapsto 7\mapsto 2\mapsto 6),(7\mapsto 7\mapsto 2\mapsto 7),(7\mapsto 7\mapsto 2\mapsto 8),(7\mapsto 7\mapsto 2\mapsto 9),(7\mapsto 7\mapsto 3\mapsto 4),(7\mapsto 7\mapsto 3\mapsto 5),(7\mapsto 7\mapsto 3\mapsto 6),(7\mapsto 7\mapsto 3\mapsto 7),(7\mapsto 7\mapsto 3\mapsto 8),(7\mapsto 7\mapsto 3\mapsto 9),(7\mapsto 7\mapsto 4\mapsto 5),(7\mapsto 7\mapsto 4\mapsto 6),(7\mapsto 7\mapsto 4\mapsto 7),(7\mapsto 7\mapsto 4\mapsto 8),(7\mapsto 7\mapsto 4\mapsto 9),(7\mapsto 7\mapsto 5\mapsto 6),(7\mapsto 7\mapsto 5\mapsto 7),(7\mapsto 7\mapsto 5\mapsto 8),(7\mapsto 7\mapsto 5\mapsto 9),(7\mapsto 7\mapsto 6\mapsto 7),(7\mapsto 7\mapsto 6\mapsto 8),(7\mapsto 7\mapsto 6\mapsto 9),(7\mapsto 7\mapsto 7\mapsto 8),(7\mapsto 7\mapsto 7\mapsto 9),(7\mapsto 7\mapsto 8\mapsto 9),(8\mapsto 8\mapsto 1\mapsto 2),(8\mapsto 8\mapsto 1\mapsto 3),(8\mapsto 8\mapsto 1\mapsto 4),(8\mapsto 8\mapsto 1\mapsto 5),(8\mapsto 8\mapsto 1\mapsto 6),(8\mapsto 8\mapsto 1\mapsto 7),(8\mapsto 8\mapsto 1\mapsto 8),(8\mapsto 8\mapsto 1\mapsto 9),(8\mapsto 8\mapsto 2\mapsto 3),(8\mapsto 8\mapsto 2\mapsto 4),(8\mapsto 8\mapsto 2\mapsto 5),(8\mapsto 8\mapsto 2\mapsto 6),(8\mapsto 8\mapsto 2\mapsto 7),(8\mapsto 8\mapsto 2\mapsto 8),(8\mapsto 8\mapsto 2\mapsto 9),(8\mapsto 8\mapsto 3\mapsto 4),(8\mapsto 8\mapsto 3\mapsto 5),(8\mapsto 8\mapsto 3\mapsto 6),(8\mapsto 8\mapsto 3\mapsto 7),(8\mapsto 8\mapsto 3\mapsto 8),(8\mapsto 8\mapsto 3\mapsto 9),(8\mapsto 8\mapsto 4\mapsto 5),(8\mapsto 8\mapsto 4\mapsto 6),(8\mapsto 8\mapsto 4\mapsto 7),(8\mapsto 8\mapsto 4\mapsto 8),(8\mapsto 8\mapsto 4\mapsto 9),(8\mapsto 8\mapsto 5\mapsto 6),(8\mapsto 8\mapsto 5\mapsto 7),(8\mapsto 8\mapsto 5\mapsto 8),(8\mapsto 8\mapsto 5\mapsto 9),(8\mapsto 8\mapsto 6\mapsto 7),(8\mapsto 8\mapsto 6\mapsto 8),(8\mapsto 8\mapsto 6\mapsto 9),(8\mapsto 8\mapsto 7\mapsto 8),(8\mapsto 8\mapsto 7\mapsto 9),(8\mapsto 8\mapsto 8\mapsto 9),(9\mapsto 9\mapsto 1\mapsto 2),(9\mapsto 9\mapsto 1\mapsto 3),(9\mapsto 9\mapsto 1\mapsto 4),(9\mapsto 9\mapsto 1\mapsto 5),(9\mapsto 9\mapsto 1\mapsto 6),(9\mapsto 9\mapsto 1\mapsto 7),(9\mapsto 9\mapsto 1\mapsto 8),(9\mapsto 9\mapsto 1\mapsto 9),(9\mapsto 9\mapsto 2\mapsto 3),(9\mapsto 9\mapsto 2\mapsto 4),(9\mapsto 9\mapsto 2\mapsto 5),(9\mapsto 9\mapsto 2\mapsto 6),(9\mapsto 9\mapsto 2\mapsto 7),(9\mapsto 9\mapsto 2\mapsto 8),(9\mapsto 9\mapsto 2\mapsto 9),(9\mapsto 9\mapsto 3\mapsto 4),(9\mapsto 9\mapsto 3\mapsto 5),(9\mapsto 9\mapsto 3\mapsto 6),(9\mapsto 9\mapsto 3\mapsto 7),(9\mapsto 9\mapsto 3\mapsto 8),(9\mapsto 9\mapsto 3\mapsto 9),(9\mapsto 9\mapsto 4\mapsto 5),(9\mapsto 9\mapsto 4\mapsto 6),(9\mapsto 9\mapsto 4\mapsto 7),(9\mapsto 9\mapsto 4\mapsto 8),(9\mapsto 9\mapsto 4\mapsto 9),(9\mapsto 9\mapsto 5\mapsto 6),(9\mapsto 9\mapsto 5\mapsto 7),(9\mapsto 9\mapsto 5\mapsto 8),(9\mapsto 9\mapsto 5\mapsto 9),(9\mapsto 9\mapsto 6\mapsto 7),(9\mapsto 9\mapsto 6\mapsto 8),(9\mapsto 9\mapsto 6\mapsto 9),(9\mapsto 9\mapsto 7\mapsto 8),(9\mapsto 9\mapsto 7\mapsto 9),(9\mapsto 9\mapsto 8\mapsto 9)\}$
{(1↦1↦1↦2),(1↦1↦1↦3),(1↦1↦1↦4),(1↦1↦1↦5),(1↦1↦1↦6),(1↦1↦1↦7),(1↦1↦1↦8),(1↦1↦1↦9),(1↦1↦2↦3),(1↦1↦2↦4),(1↦1↦2↦5),(1↦1↦2↦6),(1↦1↦2↦7),(1↦1↦2↦8),(1↦1↦2↦9),(1↦1↦3↦4),(1↦1↦3↦5),(1↦1↦3↦6),(1↦1↦3↦7),(1↦1↦3↦8),(1↦1↦3↦9),(1↦1↦4↦5),(1↦1↦4↦6),(1↦1↦4↦7),(1↦1↦4↦8),(1↦1↦4↦9),(1↦1↦5↦6),(1↦1↦5↦7),(1↦1↦5↦8),(1↦1↦5↦9),(1↦1↦6↦7),(1↦1↦6↦8),(1↦1↦6↦9),(1↦1↦7↦8),(1↦1↦7↦9),(1↦1↦8↦9),(2↦2↦1↦2),(2↦2↦1↦3),(2↦2↦1↦4),(2↦2↦1↦5),(2↦2↦1↦6),(2↦2↦1↦7),(2↦2↦1↦8),(2↦2↦1↦9),(2↦2↦2↦3),(2↦2↦2↦4),(2↦2↦2↦5),(2↦2↦2↦6),(2↦2↦2↦7),(2↦2↦2↦8),(2↦2↦2↦9),(2↦2↦3↦4),(2↦2↦3↦5),(2↦2↦3↦6),(2↦2↦3↦7),(2↦2↦3↦8),(2↦2↦3↦9),(2↦2↦4↦5),(2↦2↦4↦6),(2↦2↦4↦7),(2↦2↦4↦8),(2↦2↦4↦9),(2↦2↦5↦6),(2↦2↦5↦7),(2↦2↦5↦8),(2↦2↦5↦9),(2↦2↦6↦7),(2↦2↦6↦8),(2↦2↦6↦9),(2↦2↦7↦8),(2↦2↦7↦9),(2↦2↦8↦9),(3↦3↦1↦2),(3↦3↦1↦3),(3↦3↦1↦4),(3↦3↦1↦5),(3↦3↦1↦6),(3↦3↦1↦7),(3↦3↦1↦8),(3↦3↦1↦9),(3↦3↦2↦3),(3↦3↦2↦4),(3↦3↦2↦5),(3↦3↦2↦6),(3↦3↦2↦7),(3↦3↦2↦8),(3↦3↦2↦9),(3↦3↦3↦4),(3↦3↦3↦5),(3↦3↦3↦6),(3↦3↦3↦7),(3↦3↦3↦8),(3↦3↦3↦9),(3↦3↦4↦5),(3↦3↦4↦6),(3↦3↦4↦7),(3↦3↦4↦8),(3↦3↦4↦9),(3↦3↦5↦6),(3↦3↦5↦7),(3↦3↦5↦8),(3↦3↦5↦9),(3↦3↦6↦7),(3↦3↦6↦8),(3↦3↦6↦9),(3↦3↦7↦8),(3↦3↦7↦9),(3↦3↦8↦9),(4↦4↦1↦2),(4↦4↦1↦3),(4↦4↦1↦4),(4↦4↦1↦5),(4↦4↦1↦6),(4↦4↦1↦7),(4↦4↦1↦8),(4↦4↦1↦9),(4↦4↦2↦3),(4↦4↦2↦4),(4↦4↦2↦5),(4↦4↦2↦6),(4↦4↦2↦7),(4↦4↦2↦8),(4↦4↦2↦9),(4↦4↦3↦4),(4↦4↦3↦5),(4↦4↦3↦6),(4↦4↦3↦7),(4↦4↦3↦8),(4↦4↦3↦9),(4↦4↦4↦5),(4↦4↦4↦6),(4↦4↦4↦7),(4↦4↦4↦8),(4↦4↦4↦9),(4↦4↦5↦6),(4↦4↦5↦7),(4↦4↦5↦8),(4↦4↦5↦9),(4↦4↦6↦7),(4↦4↦6↦8),(4↦4↦6↦9),(4↦4↦7↦8),(4↦4↦7↦9),(4↦4↦8↦9),(5↦5↦1↦2),(5↦5↦1↦3),(5↦5↦1↦4),(5↦5↦1↦5),(5↦5↦1↦6),(5↦5↦1↦7),(5↦5↦1↦8),(5↦5↦1↦9),(5↦5↦2↦3),(5↦5↦2↦4),(5↦5↦2↦5),(5↦5↦2↦6),(5↦5↦2↦7),(5↦5↦2↦8),(5↦5↦2↦9),(5↦5↦3↦4),(5↦5↦3↦5),(5↦5↦3↦6),(5↦5↦3↦7),(5↦5↦3↦8),(5↦5↦3↦9),(5↦5↦4↦5),(5↦5↦4↦6),(5↦5↦4↦7),(5↦5↦4↦8),(5↦5↦4↦9),(5↦5↦5↦6),(5↦5↦5↦7),(5↦5↦5↦8),(5↦5↦5↦9),(5↦5↦6↦7),(5↦5↦6↦8),(5↦5↦6↦9),(5↦5↦7↦8),(5↦5↦7↦9),(5↦5↦8↦9),(6↦6↦1↦2),(6↦6↦1↦3),(6↦6↦1↦4),(6↦6↦1↦5),(6↦6↦1↦6),(6↦6↦1↦7),(6↦6↦1↦8),(6↦6↦1↦9),(6↦6↦2↦3),(6↦6↦2↦4),(6↦6↦2↦5),(6↦6↦2↦6),(6↦6↦2↦7),(6↦6↦2↦8),(6↦6↦2↦9),(6↦6↦3↦4),(6↦6↦3↦5),(6↦6↦3↦6),(6↦6↦3↦7),(6↦6↦3↦8),(6↦6↦3↦9),(6↦6↦4↦5),(6↦6↦4↦6),(6↦6↦4↦7),(6↦6↦4↦8),(6↦6↦4↦9),(6↦6↦5↦6),(6↦6↦5↦7),(6↦6↦5↦8),(6↦6↦5↦9),(6↦6↦6↦7),(6↦6↦6↦8),(6↦6↦6↦9),(6↦6↦7↦8),(6↦6↦7↦9),(6↦6↦8↦9),(7↦7↦1↦2),(7↦7↦1↦3),(7↦7↦1↦4),(7↦7↦1↦5),(7↦7↦1↦6),(7↦7↦1↦7),(7↦7↦1↦8),(7↦7↦1↦9),(7↦7↦2↦3),(7↦7↦2↦4),(7↦7↦2↦5),(7↦7↦2↦6),(7↦7↦2↦7),(7↦7↦2↦8),(7↦7↦2↦9),(7↦7↦3↦4),(7↦7↦3↦5),(7↦7↦3↦6),(7↦7↦3↦7),(7↦7↦3↦8),(7↦7↦3↦9),(7↦7↦4↦5),(7↦7↦4↦6),(7↦7↦4↦7),(7↦7↦4↦8),(7↦7↦4↦9),(7↦7↦5↦6),(7↦7↦5↦7),(7↦7↦5↦8),(7↦7↦5↦9),(7↦7↦6↦7),(7↦7↦6↦8),(7↦7↦6↦9),(7↦7↦7↦8),(7↦7↦7↦9),(7↦7↦8↦9),(8↦8↦1↦2),(8↦8↦1↦3),(8↦8↦1↦4),(8↦8↦1↦5),(8↦8↦1↦6),(8↦8↦1↦7),(8↦8↦1↦8),(8↦8↦1↦9),(8↦8↦2↦3),(8↦8↦2↦4),(8↦8↦2↦5),(8↦8↦2↦6),(8↦8↦2↦7),(8↦8↦2↦8),(8↦8↦2↦9),(8↦8↦3↦4),(8↦8↦3↦5),(8↦8↦3↦6),(8↦8↦3↦7),(8↦8↦3↦8),(8↦8↦3↦9),(8↦8↦4↦5),(8↦8↦4↦6),(8↦8↦4↦7),(8↦8↦4↦8),(8↦8↦4↦9),(8↦8↦5↦6),(8↦8↦5↦7),(8↦8↦5↦8),(8↦8↦5↦9),(8↦8↦6↦7),(8↦8↦6↦8),(8↦8↦6↦9),(8↦8↦7↦8),(8↦8↦7↦9),(8↦8↦8↦9),(9↦9↦1↦2),(9↦9↦1↦3),(9↦9↦1↦4),(9↦9↦1↦5),(9↦9↦1↦6),(9↦9↦1↦7),(9↦9↦1↦8),(9↦9↦1↦9),(9↦9↦2↦3),(9↦9↦2↦4),(9↦9↦2↦5),(9↦9↦2↦6),(9↦9↦2↦7),(9↦9↦2↦8),(9↦9↦2↦9),(9↦9↦3↦4),(9↦9↦3↦5),(9↦9↦3↦6),(9↦9↦3↦7),(9↦9↦3↦8),(9↦9↦3↦9),(9↦9↦4↦5),(9↦9↦4↦6),(9↦9↦4↦7),(9↦9↦4↦8),(9↦9↦4↦9),(9↦9↦5↦6),(9↦9↦5↦7),(9↦9↦5↦8),(9↦9↦5↦9),(9↦9↦6↦7),(9↦9↦6↦8),(9↦9↦6↦9),(9↦9↦7↦8),(9↦9↦7↦9),(9↦9↦8↦9)}
%% Cell type:markdown id: tags:
We have not yet encoded that in each sub-square the values must also all be distinct. Nonetheless, let us try and solve the puzzle as it stands, by looking for a full board (of type `DOM → (DOM → DOM)`) which has distinct values on each row and column:
%% Cell type:code id: tags:
``` prob
Board : DOM --> (DOM --> DOM) & !(x1,x2,y1,y2).((x1,x2,y1,y2):Diff1\/Diff2 => Board(x1)(y1) /= Board(x2)(y2))
```
%% Output
$\mathit{TRUE}$
**Solution:**
* $\mathit{Diff2} = \{(1\mapsto 1\mapsto 1\mapsto 2),(1\mapsto 1\mapsto 1\mapsto 3),(1\mapsto 1\mapsto 1\mapsto 4),(1\mapsto 1\mapsto 1\mapsto 5),(1\mapsto 1\mapsto 1\mapsto 6),(1\mapsto 1\mapsto 1\mapsto 7),(1\mapsto 1\mapsto 1\mapsto 8),(1\mapsto 1\mapsto 1\mapsto 9),(1\mapsto 1\mapsto 2\mapsto 3),(1\mapsto 1\mapsto 2\mapsto 4),(1\mapsto 1\mapsto 2\mapsto 5),(1\mapsto 1\mapsto 2\mapsto 6),(1\mapsto 1\mapsto 2\mapsto 7),(1\mapsto 1\mapsto 2\mapsto 8),(1\mapsto 1\mapsto 2\mapsto 9),(1\mapsto 1\mapsto 3\mapsto 4),(1\mapsto 1\mapsto 3\mapsto 5),(1\mapsto 1\mapsto 3\mapsto 6),(1\mapsto 1\mapsto 3\mapsto 7),(1\mapsto 1\mapsto 3\mapsto 8),(1\mapsto 1\mapsto 3\mapsto 9),(1\mapsto 1\mapsto 4\mapsto 5),(1\mapsto 1\mapsto 4\mapsto 6),(1\mapsto 1\mapsto 4\mapsto 7),(1\mapsto 1\mapsto 4\mapsto 8),(1\mapsto 1\mapsto 4\mapsto 9),(1\mapsto 1\mapsto 5\mapsto 6),(1\mapsto 1\mapsto 5\mapsto 7),(1\mapsto 1\mapsto 5\mapsto 8),(1\mapsto 1\mapsto 5\mapsto 9),(1\mapsto 1\mapsto 6\mapsto 7),(1\mapsto 1\mapsto 6\mapsto 8),(1\mapsto 1\mapsto 6\mapsto 9),(1\mapsto 1\mapsto 7\mapsto 8),(1\mapsto 1\mapsto 7\mapsto 9),(1\mapsto 1\mapsto 8\mapsto 9),(2\mapsto 2\mapsto 1\mapsto 2),(2\mapsto 2\mapsto 1\mapsto 3),(2\mapsto 2\mapsto 1\mapsto 4),(2\mapsto 2\mapsto 1\mapsto 5),(2\mapsto 2\mapsto 1\mapsto 6),(2\mapsto 2\mapsto 1\mapsto 7),(2\mapsto 2\mapsto 1\mapsto 8),(2\mapsto 2\mapsto 1\mapsto 9),(2\mapsto 2\mapsto 2\mapsto 3),(2\mapsto 2\mapsto 2\mapsto 4),(2\mapsto 2\mapsto 2\mapsto 5),(2\mapsto 2\mapsto 2\mapsto 6),(2\mapsto 2\mapsto 2\mapsto 7),(2\mapsto 2\mapsto 2\mapsto 8),(2\mapsto 2\mapsto 2\mapsto 9),(2\mapsto 2\mapsto 3\mapsto 4),(2\mapsto 2\mapsto 3\mapsto 5),(2\mapsto 2\mapsto 3\mapsto 6),(2\mapsto 2\mapsto 3\mapsto 7),(2\mapsto 2\mapsto 3\mapsto 8),(2\mapsto 2\mapsto 3\mapsto 9),(2\mapsto 2\mapsto 4\mapsto 5),(2\mapsto 2\mapsto 4\mapsto 6),(2\mapsto 2\mapsto 4\mapsto 7),(2\mapsto 2\mapsto 4\mapsto 8),(2\mapsto 2\mapsto 4\mapsto 9),(2\mapsto 2\mapsto 5\mapsto 6),(2\mapsto 2\mapsto 5\mapsto 7),(2\mapsto 2\mapsto 5\mapsto 8),(2\mapsto 2\mapsto 5\mapsto 9),(2\mapsto 2\mapsto 6\mapsto 7),(2\mapsto 2\mapsto 6\mapsto 8),(2\mapsto 2\mapsto 6\mapsto 9),(2\mapsto 2\mapsto 7\mapsto 8),(2\mapsto 2\mapsto 7\mapsto 9),(2\mapsto 2\mapsto 8\mapsto 9),(3\mapsto 3\mapsto 1\mapsto 2),(3\mapsto 3\mapsto 1\mapsto 3),(3\mapsto 3\mapsto 1\mapsto 4),(3\mapsto 3\mapsto 1\mapsto 5),(3\mapsto 3\mapsto 1\mapsto 6),(3\mapsto 3\mapsto 1\mapsto 7),(3\mapsto 3\mapsto 1\mapsto 8),(3\mapsto 3\mapsto 1\mapsto 9),(3\mapsto 3\mapsto 2\mapsto 3),(3\mapsto 3\mapsto 2\mapsto 4),(3\mapsto 3\mapsto 2\mapsto 5),(3\mapsto 3\mapsto 2\mapsto 6),(3\mapsto 3\mapsto 2\mapsto 7),(3\mapsto 3\mapsto 2\mapsto 8),(3\mapsto 3\mapsto 2\mapsto 9),(3\mapsto 3\mapsto 3\mapsto 4),(3\mapsto 3\mapsto 3\mapsto 5),(3\mapsto 3\mapsto 3\mapsto 6),(3\mapsto 3\mapsto 3\mapsto 7),(3\mapsto 3\mapsto 3\mapsto 8),(3\mapsto 3\mapsto 3\mapsto 9),(3\mapsto 3\mapsto 4\mapsto 5),(3\mapsto 3\mapsto 4\mapsto 6),(3\mapsto 3\mapsto 4\mapsto 7),(3\mapsto 3\mapsto 4\mapsto 8),(3\mapsto 3\mapsto 4\mapsto 9),(3\mapsto 3\mapsto 5\mapsto 6),(3\mapsto 3\mapsto 5\mapsto 7),(3\mapsto 3\mapsto 5\mapsto 8),(3\mapsto 3\mapsto 5\mapsto 9),(3\mapsto 3\mapsto 6\mapsto 7),(3\mapsto 3\mapsto 6\mapsto 8),(3\mapsto 3\mapsto 6\mapsto 9),(3\mapsto 3\mapsto 7\mapsto 8),(3\mapsto 3\mapsto 7\mapsto 9),(3\mapsto 3\mapsto 8\mapsto 9),(4\mapsto 4\mapsto 1\mapsto 2),(4\mapsto 4\mapsto 1\mapsto 3),(4\mapsto 4\mapsto 1\mapsto 4),(4\mapsto 4\mapsto 1\mapsto 5),(4\mapsto 4\mapsto 1\mapsto 6),(4\mapsto 4\mapsto 1\mapsto 7),(4\mapsto 4\mapsto 1\mapsto 8),(4\mapsto 4\mapsto 1\mapsto 9),(4\mapsto 4\mapsto 2\mapsto 3),(4\mapsto 4\mapsto 2\mapsto 4),(4\mapsto 4\mapsto 2\mapsto 5),(4\mapsto 4\mapsto 2\mapsto 6),(4\mapsto 4\mapsto 2\mapsto 7),(4\mapsto 4\mapsto 2\mapsto 8),(4\mapsto 4\mapsto 2\mapsto 9),(4\mapsto 4\mapsto 3\mapsto 4),(4\mapsto 4\mapsto 3\mapsto 5),(4\mapsto 4\mapsto 3\mapsto 6),(4\mapsto 4\mapsto 3\mapsto 7),(4\mapsto 4\mapsto 3\mapsto 8),(4\mapsto 4\mapsto 3\mapsto 9),(4\mapsto 4\mapsto 4\mapsto 5),(4\mapsto 4\mapsto 4\mapsto 6),(4\mapsto 4\mapsto 4\mapsto 7),(4\mapsto 4\mapsto 4\mapsto 8),(4\mapsto 4\mapsto 4\mapsto 9),(4\mapsto 4\mapsto 5\mapsto 6),(4\mapsto 4\mapsto 5\mapsto 7),(4\mapsto 4\mapsto 5\mapsto 8),(4\mapsto 4\mapsto 5\mapsto 9),(4\mapsto 4\mapsto 6\mapsto 7),(4\mapsto 4\mapsto 6\mapsto 8),(4\mapsto 4\mapsto 6\mapsto 9),(4\mapsto 4\mapsto 7\mapsto 8),(4\mapsto 4\mapsto 7\mapsto 9),(4\mapsto 4\mapsto 8\mapsto 9),(5\mapsto 5\mapsto 1\mapsto 2),(5\mapsto 5\mapsto 1\mapsto 3),(5\mapsto 5\mapsto 1\mapsto 4),(5\mapsto 5\mapsto 1\mapsto 5),(5\mapsto 5\mapsto 1\mapsto 6),(5\mapsto 5\mapsto 1\mapsto 7),(5\mapsto 5\mapsto 1\mapsto 8),(5\mapsto 5\mapsto 1\mapsto 9),(5\mapsto 5\mapsto 2\mapsto 3),(5\mapsto 5\mapsto 2\mapsto 4),(5\mapsto 5\mapsto 2\mapsto 5),(5\mapsto 5\mapsto 2\mapsto 6),(5\mapsto 5\mapsto 2\mapsto 7),(5\mapsto 5\mapsto 2\mapsto 8),(5\mapsto 5\mapsto 2\mapsto 9),(5\mapsto 5\mapsto 3\mapsto 4),(5\mapsto 5\mapsto 3\mapsto 5),(5\mapsto 5\mapsto 3\mapsto 6),(5\mapsto 5\mapsto 3\mapsto 7),(5\mapsto 5\mapsto 3\mapsto 8),(5\mapsto 5\mapsto 3\mapsto 9),(5\mapsto 5\mapsto 4\mapsto 5),(5\mapsto 5\mapsto 4\mapsto 6),(5\mapsto 5\mapsto 4\mapsto 7),(5\mapsto 5\mapsto 4\mapsto 8),(5\mapsto 5\mapsto 4\mapsto 9),(5\mapsto 5\mapsto 5\mapsto 6),(5\mapsto 5\mapsto 5\mapsto 7),(5\mapsto 5\mapsto 5\mapsto 8),(5\mapsto 5\mapsto 5\mapsto 9),(5\mapsto 5\mapsto 6\mapsto 7),(5\mapsto 5\mapsto 6\mapsto 8),(5\mapsto 5\mapsto 6\mapsto 9),(5\mapsto 5\mapsto 7\mapsto 8),(5\mapsto 5\mapsto 7\mapsto 9),(5\mapsto 5\mapsto 8\mapsto 9),(6\mapsto 6\mapsto 1\mapsto 2),(6\mapsto 6\mapsto 1\mapsto 3),(6\mapsto 6\mapsto 1\mapsto 4),(6\mapsto 6\mapsto 1\mapsto 5),(6\mapsto 6\mapsto 1\mapsto 6),(6\mapsto 6\mapsto 1\mapsto 7),(6\mapsto 6\mapsto 1\mapsto 8),(6\mapsto 6\mapsto 1\mapsto 9),(6\mapsto 6\mapsto 2\mapsto 3),(6\mapsto 6\mapsto 2\mapsto 4),(6\mapsto 6\mapsto 2\mapsto 5),(6\mapsto 6\mapsto 2\mapsto 6),(6\mapsto 6\mapsto 2\mapsto 7),(6\mapsto 6\mapsto 2\mapsto 8),(6\mapsto 6\mapsto 2\mapsto 9),(6\mapsto 6\mapsto 3\mapsto 4),(6\mapsto 6\mapsto 3\mapsto 5),(6\mapsto 6\mapsto 3\mapsto 6),(6\mapsto 6\mapsto 3\mapsto 7),(6\mapsto 6\mapsto 3\mapsto 8),(6\mapsto 6\mapsto 3\mapsto 9),(6\mapsto 6\mapsto 4\mapsto 5),(6\mapsto 6\mapsto 4\mapsto 6),(6\mapsto 6\mapsto 4\mapsto 7),(6\mapsto 6\mapsto 4\mapsto 8),(6\mapsto 6\mapsto 4\mapsto 9),(6\mapsto 6\mapsto 5\mapsto 6),(6\mapsto 6\mapsto 5\mapsto 7),(6\mapsto 6\mapsto 5\mapsto 8),(6\mapsto 6\mapsto 5\mapsto 9),(6\mapsto 6\mapsto 6\mapsto 7),(6\mapsto 6\mapsto 6\mapsto 8),(6\mapsto 6\mapsto 6\mapsto 9),(6\mapsto 6\mapsto 7\mapsto 8),(6\mapsto 6\mapsto 7\mapsto 9),(6\mapsto 6\mapsto 8\mapsto 9),(7\mapsto 7\mapsto 1\mapsto 2),(7\mapsto 7\mapsto 1\mapsto 3),(7\mapsto 7\mapsto 1\mapsto 4),(7\mapsto 7\mapsto 1\mapsto 5),(7\mapsto 7\mapsto 1\mapsto 6),(7\mapsto 7\mapsto 1\mapsto 7),(7\mapsto 7\mapsto 1\mapsto 8),(7\mapsto 7\mapsto 1\mapsto 9),(7\mapsto 7\mapsto 2\mapsto 3),(7\mapsto 7\mapsto 2\mapsto 4),(7\mapsto 7\mapsto 2\mapsto 5),(7\mapsto 7\mapsto 2\mapsto 6),(7\mapsto 7\mapsto 2\mapsto 7),(7\mapsto 7\mapsto 2\mapsto 8),(7\mapsto 7\mapsto 2\mapsto 9),(7\mapsto 7\mapsto 3\mapsto 4),(7\mapsto 7\mapsto 3\mapsto 5),(7\mapsto 7\mapsto 3\mapsto 6),(7\mapsto 7\mapsto 3\mapsto 7),(7\mapsto 7\mapsto 3\mapsto 8),(7\mapsto 7\mapsto 3\mapsto 9),(7\mapsto 7\mapsto 4\mapsto 5),(7\mapsto 7\mapsto 4\mapsto 6),(7\mapsto 7\mapsto 4\mapsto 7),(7\mapsto 7\mapsto 4\mapsto 8),(7\mapsto 7\mapsto 4\mapsto 9),(7\mapsto 7\mapsto 5\mapsto 6),(7\mapsto 7\mapsto 5\mapsto 7),(7\mapsto 7\mapsto 5\mapsto 8),(7\mapsto 7\mapsto 5\mapsto 9),(7\mapsto 7\mapsto 6\mapsto 7),(7\mapsto 7\mapsto 6\mapsto 8),(7\mapsto 7\mapsto 6\mapsto 9),(7\mapsto 7\mapsto 7\mapsto 8),(7\mapsto 7\mapsto 7\mapsto 9),(7\mapsto 7\mapsto 8\mapsto 9),(8\mapsto 8\mapsto 1\mapsto 2),(8\mapsto 8\mapsto 1\mapsto 3),(8\mapsto 8\mapsto 1\mapsto 4),(8\mapsto 8\mapsto 1\mapsto 5),(8\mapsto 8\mapsto 1\mapsto 6),(8\mapsto 8\mapsto 1\mapsto 7),(8\mapsto 8\mapsto 1\mapsto 8),(8\mapsto 8\mapsto 1\mapsto 9),(8\mapsto 8\mapsto 2\mapsto 3),(8\mapsto 8\mapsto 2\mapsto 4),(8\mapsto 8\mapsto 2\mapsto 5),(8\mapsto 8\mapsto 2\mapsto 6),(8\mapsto 8\mapsto 2\mapsto 7),(8\mapsto 8\mapsto 2\mapsto 8),(8\mapsto 8\mapsto 2\mapsto 9),(8\mapsto 8\mapsto 3\mapsto 4),(8\mapsto 8\mapsto 3\mapsto 5),(8\mapsto 8\mapsto 3\mapsto 6),(8\mapsto 8\mapsto 3\mapsto 7),(8\mapsto 8\mapsto 3\mapsto 8),(8\mapsto 8\mapsto 3\mapsto 9),(8\mapsto 8\mapsto 4\mapsto 5),(8\mapsto 8\mapsto 4\mapsto 6),(8\mapsto 8\mapsto 4\mapsto 7),(8\mapsto 8\mapsto 4\mapsto 8),(8\mapsto 8\mapsto 4\mapsto 9),(8\mapsto 8\mapsto 5\mapsto 6),(8\mapsto 8\mapsto 5\mapsto 7),(8\mapsto 8\mapsto 5\mapsto 8),(8\mapsto 8\mapsto 5\mapsto 9),(8\mapsto 8\mapsto 6\mapsto 7),(8\mapsto 8\mapsto 6\mapsto 8),(8\mapsto 8\mapsto 6\mapsto 9),(8\mapsto 8\mapsto 7\mapsto 8),(8\mapsto 8\mapsto 7\mapsto 9),(8\mapsto 8\mapsto 8\mapsto 9),(9\mapsto 9\mapsto 1\mapsto 2),(9\mapsto 9\mapsto 1\mapsto 3),(9\mapsto 9\mapsto 1\mapsto 4),(9\mapsto 9\mapsto 1\mapsto 5),(9\mapsto 9\mapsto 1\mapsto 6),(9\mapsto 9\mapsto 1\mapsto 7),(9\mapsto 9\mapsto 1\mapsto 8),(9\mapsto 9\mapsto 1\mapsto 9),(9\mapsto 9\mapsto 2\mapsto 3),(9\mapsto 9\mapsto 2\mapsto 4),(9\mapsto 9\mapsto 2\mapsto 5),(9\mapsto 9\mapsto 2\mapsto 6),(9\mapsto 9\mapsto 2\mapsto 7),(9\mapsto 9\mapsto 2\mapsto 8),(9\mapsto 9\mapsto 2\mapsto 9),(9\mapsto 9\mapsto 3\mapsto 4),(9\mapsto 9\mapsto 3\mapsto 5),(9\mapsto 9\mapsto 3\mapsto 6),(9\mapsto 9\mapsto 3\mapsto 7),(9\mapsto 9\mapsto 3\mapsto 8),(9\mapsto 9\mapsto 3\mapsto 9),(9\mapsto 9\mapsto 4\mapsto 5),(9\mapsto 9\mapsto 4\mapsto 6),(9\mapsto 9\mapsto 4\mapsto 7),(9\mapsto 9\mapsto 4\mapsto 8),(9\mapsto 9\mapsto 4\mapsto 9),(9\mapsto 9\mapsto 5\mapsto 6),(9\mapsto 9\mapsto 5\mapsto 7),(9\mapsto 9\mapsto 5\mapsto 8),(9\mapsto 9\mapsto 5\mapsto 9),(9\mapsto 9\mapsto 6\mapsto 7),(9\mapsto 9\mapsto 6\mapsto 8),(9\mapsto 9\mapsto 6\mapsto 9),(9\mapsto 9\mapsto 7\mapsto 8),(9\mapsto 9\mapsto 7\mapsto 9),(9\mapsto 9\mapsto 8\mapsto 9)\}$
* $\mathit{Board} = \{(1\mapsto\{(1\mapsto 2),(2\mapsto 5),(3\mapsto 4),(4\mapsto 1),(5\mapsto 3),(6\mapsto 6),(7\mapsto 7),(8\mapsto 8),(9\mapsto 9)\}),(2\mapsto\{(1\mapsto 1),(2\mapsto 4),(3\mapsto 2),(4\mapsto 3),(5\mapsto 6),(6\mapsto 5),(7\mapsto 9),(8\mapsto 7),(9\mapsto 8)\}),(3\mapsto\{(1\mapsto 4),(2\mapsto 9),(3\mapsto 3),(4\mapsto 2),(5\mapsto 1),(6\mapsto 8),(7\mapsto 5),(8\mapsto 6),(9\mapsto 7)\}),(4\mapsto\{(1\mapsto 3),(2\mapsto 1),(3\mapsto 8),(4\mapsto 7),(5\mapsto 9),(6\mapsto 2),(7\mapsto 4),(8\mapsto 5),(9\mapsto 6)\}),(5\mapsto\{(1\mapsto 6),(2\mapsto 3),(3\mapsto 9),(4\mapsto 8),(5\mapsto 7),(6\mapsto 1),(7\mapsto 2),(8\mapsto 4),(9\mapsto 5)\}),(6\mapsto\{(1\mapsto 5),(2\mapsto 2),(3\mapsto 1),(4\mapsto 9),(5\mapsto 8),(6\mapsto 7),(7\mapsto 6),(8\mapsto 3),(9\mapsto 4)\}),(7\mapsto\{(1\mapsto 7),(2\mapsto 6),(3\mapsto 5),(4\mapsto 4),(5\mapsto 2),(6\mapsto 9),(7\mapsto 8),(8\mapsto 1),(9\mapsto 3)\}),(8\mapsto\{(1\mapsto 8),(2\mapsto 7),(3\mapsto 6),(4\mapsto 5),(5\mapsto 4),(6\mapsto 3),(7\mapsto 1),(8\mapsto 9),(9\mapsto 2)\}),(9\mapsto\{(1\mapsto 9),(2\mapsto 8),(3\mapsto 7),(4\mapsto 6),(5\mapsto 5),(6\mapsto 4),(7\mapsto 3),(8\mapsto 2),(9\mapsto 1)\})\}$
* $\mathit{DOM} = \{1,2,3,4,5,6,7,8,9\}$
* $\mathit{Diff1} = \{(1\mapsto 2\mapsto 1\mapsto 1),(1\mapsto 2\mapsto 2\mapsto 2),(1\mapsto 2\mapsto 3\mapsto 3),(1\mapsto 2\mapsto 4\mapsto 4),(1\mapsto 2\mapsto 5\mapsto 5),(1\mapsto 2\mapsto 6\mapsto 6),(1\mapsto 2\mapsto 7\mapsto 7),(1\mapsto 2\mapsto 8\mapsto 8),(1\mapsto 2\mapsto 9\mapsto 9),(1\mapsto 3\mapsto 1\mapsto 1),(1\mapsto 3\mapsto 2\mapsto 2),(1\mapsto 3\mapsto 3\mapsto 3),(1\mapsto 3\mapsto 4\mapsto 4),(1\mapsto 3\mapsto 5\mapsto 5),(1\mapsto 3\mapsto 6\mapsto 6),(1\mapsto 3\mapsto 7\mapsto 7),(1\mapsto 3\mapsto 8\mapsto 8),(1\mapsto 3\mapsto 9\mapsto 9),(1\mapsto 4\mapsto 1\mapsto 1),(1\mapsto 4\mapsto 2\mapsto 2),(1\mapsto 4\mapsto 3\mapsto 3),(1\mapsto 4\mapsto 4\mapsto 4),(1\mapsto 4\mapsto 5\mapsto 5),(1\mapsto 4\mapsto 6\mapsto 6),(1\mapsto 4\mapsto 7\mapsto 7),(1\mapsto 4\mapsto 8\mapsto 8),(1\mapsto 4\mapsto 9\mapsto 9),(1\mapsto 5\mapsto 1\mapsto 1),(1\mapsto 5\mapsto 2\mapsto 2),(1\mapsto 5\mapsto 3\mapsto 3),(1\mapsto 5\mapsto 4\mapsto 4),(1\mapsto 5\mapsto 5\mapsto 5),(1\mapsto 5\mapsto 6\mapsto 6),(1\mapsto 5\mapsto 7\mapsto 7),(1\mapsto 5\mapsto 8\mapsto 8),(1\mapsto 5\mapsto 9\mapsto 9),(1\mapsto 6\mapsto 1\mapsto 1),(1\mapsto 6\mapsto 2\mapsto 2),(1\mapsto 6\mapsto 3\mapsto 3),(1\mapsto 6\mapsto 4\mapsto 4),(1\mapsto 6\mapsto 5\mapsto 5),(1\mapsto 6\mapsto 6\mapsto 6),(1\mapsto 6\mapsto 7\mapsto 7),(1\mapsto 6\mapsto 8\mapsto 8),(1\mapsto 6\mapsto 9\mapsto 9),(1\mapsto 7\mapsto 1\mapsto 1),(1\mapsto 7\mapsto 2\mapsto 2),(1\mapsto 7\mapsto 3\mapsto 3),(1\mapsto 7\mapsto 4\mapsto 4),(1\mapsto 7\mapsto 5\mapsto 5),(1\mapsto 7\mapsto 6\mapsto 6),(1\mapsto 7\mapsto 7\mapsto 7),(1\mapsto 7\mapsto 8\mapsto 8),(1\mapsto 7\mapsto 9\mapsto 9),(1\mapsto 8\mapsto 1\mapsto 1),(1\mapsto 8\mapsto 2\mapsto 2),(1\mapsto 8\mapsto 3\mapsto 3),(1\mapsto 8\mapsto 4\mapsto 4),(1\mapsto 8\mapsto 5\mapsto 5),(1\mapsto 8\mapsto 6\mapsto 6),(1\mapsto 8\mapsto 7\mapsto 7),(1\mapsto 8\mapsto 8\mapsto 8),(1\mapsto 8\mapsto 9\mapsto 9),(1\mapsto 9\mapsto 1\mapsto 1),(1\mapsto 9\mapsto 2\mapsto 2),(1\mapsto 9\mapsto 3\mapsto 3),(1\mapsto 9\mapsto 4\mapsto 4),(1\mapsto 9\mapsto 5\mapsto 5),(1\mapsto 9\mapsto 6\mapsto 6),(1\mapsto 9\mapsto 7\mapsto 7),(1\mapsto 9\mapsto 8\mapsto 8),(1\mapsto 9\mapsto 9\mapsto 9),(2\mapsto 3\mapsto 1\mapsto 1),(2\mapsto 3\mapsto 2\mapsto 2),(2\mapsto 3\mapsto 3\mapsto 3),(2\mapsto 3\mapsto 4\mapsto 4),(2\mapsto 3\mapsto 5\mapsto 5),(2\mapsto 3\mapsto 6\mapsto 6),(2\mapsto 3\mapsto 7\mapsto 7),(2\mapsto 3\mapsto 8\mapsto 8),(2\mapsto 3\mapsto 9\mapsto 9),(2\mapsto 4\mapsto 1\mapsto 1),(2\mapsto 4\mapsto 2\mapsto 2),(2\mapsto 4\mapsto 3\mapsto 3),(2\mapsto 4\mapsto 4\mapsto 4),(2\mapsto 4\mapsto 5\mapsto 5),(2\mapsto 4\mapsto 6\mapsto 6),(2\mapsto 4\mapsto 7\mapsto 7),(2\mapsto 4\mapsto 8\mapsto 8),(2\mapsto 4\mapsto 9\mapsto 9),(2\mapsto 5\mapsto 1\mapsto 1),(2\mapsto 5\mapsto 2\mapsto 2),(2\mapsto 5\mapsto 3\mapsto 3),(2\mapsto 5\mapsto 4\mapsto 4),(2\mapsto 5\mapsto 5\mapsto 5),(2\mapsto 5\mapsto 6\mapsto 6),(2\mapsto 5\mapsto 7\mapsto 7),(2\mapsto 5\mapsto 8\mapsto 8),(2\mapsto 5\mapsto 9\mapsto 9),(2\mapsto 6\mapsto 1\mapsto 1),(2\mapsto 6\mapsto 2\mapsto 2),(2\mapsto 6\mapsto 3\mapsto 3),(2\mapsto 6\mapsto 4\mapsto 4),(2\mapsto 6\mapsto 5\mapsto 5),(2\mapsto 6\mapsto 6\mapsto 6),(2\mapsto 6\mapsto 7\mapsto 7),(2\mapsto 6\mapsto 8\mapsto 8),(2\mapsto 6\mapsto 9\mapsto 9),(2\mapsto 7\mapsto 1\mapsto 1),(2\mapsto 7\mapsto 2\mapsto 2),(2\mapsto 7\mapsto 3\mapsto 3),(2\mapsto 7\mapsto 4\mapsto 4),(2\mapsto 7\mapsto 5\mapsto 5),(2\mapsto 7\mapsto 6\mapsto 6),(2\mapsto 7\mapsto 7\mapsto 7),(2\mapsto 7\mapsto 8\mapsto 8),(2\mapsto 7\mapsto 9\mapsto 9),(2\mapsto 8\mapsto 1\mapsto 1),(2\mapsto 8\mapsto 2\mapsto 2),(2\mapsto 8\mapsto 3\mapsto 3),(2\mapsto 8\mapsto 4\mapsto 4),(2\mapsto 8\mapsto 5\mapsto 5),(2\mapsto 8\mapsto 6\mapsto 6),(2\mapsto 8\mapsto 7\mapsto 7),(2\mapsto 8\mapsto 8\mapsto 8),(2\mapsto 8\mapsto 9\mapsto 9),(2\mapsto 9\mapsto 1\mapsto 1),(2\mapsto 9\mapsto 2\mapsto 2),(2\mapsto 9\mapsto 3\mapsto 3),(2\mapsto 9\mapsto 4\mapsto 4),(2\mapsto 9\mapsto 5\mapsto 5),(2\mapsto 9\mapsto 6\mapsto 6),(2\mapsto 9\mapsto 7\mapsto 7),(2\mapsto 9\mapsto 8\mapsto 8),(2\mapsto 9\mapsto 9\mapsto 9),(3\mapsto 4\mapsto 1\mapsto 1),(3\mapsto 4\mapsto 2\mapsto 2),(3\mapsto 4\mapsto 3\mapsto 3),(3\mapsto 4\mapsto 4\mapsto 4),(3\mapsto 4\mapsto 5\mapsto 5),(3\mapsto 4\mapsto 6\mapsto 6),(3\mapsto 4\mapsto 7\mapsto 7),(3\mapsto 4\mapsto 8\mapsto 8),(3\mapsto 4\mapsto 9\mapsto 9),(3\mapsto 5\mapsto 1\mapsto 1),(3\mapsto 5\mapsto 2\mapsto 2),(3\mapsto 5\mapsto 3\mapsto 3),(3\mapsto 5\mapsto 4\mapsto 4),(3\mapsto 5\mapsto 5\mapsto 5),(3\mapsto 5\mapsto 6\mapsto 6),(3\mapsto 5\mapsto 7\mapsto 7),(3\mapsto 5\mapsto 8\mapsto 8),(3\mapsto 5\mapsto 9\mapsto 9),(3\mapsto 6\mapsto 1\mapsto 1),(3\mapsto 6\mapsto 2\mapsto 2),(3\mapsto 6\mapsto 3\mapsto 3),(3\mapsto 6\mapsto 4\mapsto 4),(3\mapsto 6\mapsto 5\mapsto 5),(3\mapsto 6\mapsto 6\mapsto 6),(3\mapsto 6\mapsto 7\mapsto 7),(3\mapsto 6\mapsto 8\mapsto 8),(3\mapsto 6\mapsto 9\mapsto 9),(3\mapsto 7\mapsto 1\mapsto 1),(3\mapsto 7\mapsto 2\mapsto 2),(3\mapsto 7\mapsto 3\mapsto 3),(3\mapsto 7\mapsto 4\mapsto 4),(3\mapsto 7\mapsto 5\mapsto 5),(3\mapsto 7\mapsto 6\mapsto 6),(3\mapsto 7\mapsto 7\mapsto 7),(3\mapsto 7\mapsto 8\mapsto 8),(3\mapsto 7\mapsto 9\mapsto 9),(3\mapsto 8\mapsto 1\mapsto 1),(3\mapsto 8\mapsto 2\mapsto 2),(3\mapsto 8\mapsto 3\mapsto 3),(3\mapsto 8\mapsto 4\mapsto 4),(3\mapsto 8\mapsto 5\mapsto 5),(3\mapsto 8\mapsto 6\mapsto 6),(3\mapsto 8\mapsto 7\mapsto 7),(3\mapsto 8\mapsto 8\mapsto 8),(3\mapsto 8\mapsto 9\mapsto 9),(3\mapsto 9\mapsto 1\mapsto 1),(3\mapsto 9\mapsto 2\mapsto 2),(3\mapsto 9\mapsto 3\mapsto 3),(3\mapsto 9\mapsto 4\mapsto 4),(3\mapsto 9\mapsto 5\mapsto 5),(3\mapsto 9\mapsto 6\mapsto 6),(3\mapsto 9\mapsto 7\mapsto 7),(3\mapsto 9\mapsto 8\mapsto 8),(3\mapsto 9\mapsto 9\mapsto 9),(4\mapsto 5\mapsto 1\mapsto 1),(4\mapsto 5\mapsto 2\mapsto 2),(4\mapsto 5\mapsto 3\mapsto 3),(4\mapsto 5\mapsto 4\mapsto 4),(4\mapsto 5\mapsto 5\mapsto 5),(4\mapsto 5\mapsto 6\mapsto 6),(4\mapsto 5\mapsto 7\mapsto 7),(4\mapsto 5\mapsto 8\mapsto 8),(4\mapsto 5\mapsto 9\mapsto 9),(4\mapsto 6\mapsto 1\mapsto 1),(4\mapsto 6\mapsto 2\mapsto 2),(4\mapsto 6\mapsto 3\mapsto 3),(4\mapsto 6\mapsto 4\mapsto 4),(4\mapsto 6\mapsto 5\mapsto 5),(4\mapsto 6\mapsto 6\mapsto 6),(4\mapsto 6\mapsto 7\mapsto 7),(4\mapsto 6\mapsto 8\mapsto 8),(4\mapsto 6\mapsto 9\mapsto 9),(4\mapsto 7\mapsto 1\mapsto 1),(4\mapsto 7\mapsto 2\mapsto 2),(4\mapsto 7\mapsto 3\mapsto 3),(4\mapsto 7\mapsto 4\mapsto 4),(4\mapsto 7\mapsto 5\mapsto 5),(4\mapsto 7\mapsto 6\mapsto 6),(4\mapsto 7\mapsto 7\mapsto 7),(4\mapsto 7\mapsto 8\mapsto 8),(4\mapsto 7\mapsto 9\mapsto 9),(4\mapsto 8\mapsto 1\mapsto 1),(4\mapsto 8\mapsto 2\mapsto 2),(4\mapsto 8\mapsto 3\mapsto 3),(4\mapsto 8\mapsto 4\mapsto 4),(4\mapsto 8\mapsto 5\mapsto 5),(4\mapsto 8\mapsto 6\mapsto 6),(4\mapsto 8\mapsto 7\mapsto 7),(4\mapsto 8\mapsto 8\mapsto 8),(4\mapsto 8\mapsto 9\mapsto 9),(4\mapsto 9\mapsto 1\mapsto 1),(4\mapsto 9\mapsto 2\mapsto 2),(4\mapsto 9\mapsto 3\mapsto 3),(4\mapsto 9\mapsto 4\mapsto 4),(4\mapsto 9\mapsto 5\mapsto 5),(4\mapsto 9\mapsto 6\mapsto 6),(4\mapsto 9\mapsto 7\mapsto 7),(4\mapsto 9\mapsto 8\mapsto 8),(4\mapsto 9\mapsto 9\mapsto 9),(5\mapsto 6\mapsto 1\mapsto 1),(5\mapsto 6\mapsto 2\mapsto 2),(5\mapsto 6\mapsto 3\mapsto 3),(5\mapsto 6\mapsto 4\mapsto 4),(5\mapsto 6\mapsto 5\mapsto 5),(5\mapsto 6\mapsto 6\mapsto 6),(5\mapsto 6\mapsto 7\mapsto 7),(5\mapsto 6\mapsto 8\mapsto 8),(5\mapsto 6\mapsto 9\mapsto 9),(5\mapsto 7\mapsto 1\mapsto 1),(5\mapsto 7\mapsto 2\mapsto 2),(5\mapsto 7\mapsto 3\mapsto 3),(5\mapsto 7\mapsto 4\mapsto 4),(5\mapsto 7\mapsto 5\mapsto 5),(5\mapsto 7\mapsto 6\mapsto 6),(5\mapsto 7\mapsto 7\mapsto 7),(5\mapsto 7\mapsto 8\mapsto 8),(5\mapsto 7\mapsto 9\mapsto 9),(5\mapsto 8\mapsto 1\mapsto 1),(5\mapsto 8\mapsto 2\mapsto 2),(5\mapsto 8\mapsto 3\mapsto 3),(5\mapsto 8\mapsto 4\mapsto 4),(5\mapsto 8\mapsto 5\mapsto 5),(5\mapsto 8\mapsto 6\mapsto 6),(5\mapsto 8\mapsto 7\mapsto 7),(5\mapsto 8\mapsto 8\mapsto 8),(5\mapsto 8\mapsto 9\mapsto 9),(5\mapsto 9\mapsto 1\mapsto 1),(5\mapsto 9\mapsto 2\mapsto 2),(5\mapsto 9\mapsto 3\mapsto 3),(5\mapsto 9\mapsto 4\mapsto 4),(5\mapsto 9\mapsto 5\mapsto 5),(5\mapsto 9\mapsto 6\mapsto 6),(5\mapsto 9\mapsto 7\mapsto 7),(5\mapsto 9\mapsto 8\mapsto 8),(5\mapsto 9\mapsto 9\mapsto 9),(6\mapsto 7\mapsto 1\mapsto 1),(6\mapsto 7\mapsto 2\mapsto 2),(6\mapsto 7\mapsto 3\mapsto 3),(6\mapsto 7\mapsto 4\mapsto 4),(6\mapsto 7\mapsto 5\mapsto 5),(6\mapsto 7\mapsto 6\mapsto 6),(6\mapsto 7\mapsto 7\mapsto 7),(6\mapsto 7\mapsto 8\mapsto 8),(6\mapsto 7\mapsto 9\mapsto 9),(6\mapsto 8\mapsto 1\mapsto 1),(6\mapsto 8\mapsto 2\mapsto 2),(6\mapsto 8\mapsto 3\mapsto 3),(6\mapsto 8\mapsto 4\mapsto 4),(6\mapsto 8\mapsto 5\mapsto 5),(6\mapsto 8\mapsto 6\mapsto 6),(6\mapsto 8\mapsto 7\mapsto 7),(6\mapsto 8\mapsto 8\mapsto 8),(6\mapsto 8\mapsto 9\mapsto 9),(6\mapsto 9\mapsto 1\mapsto 1),(6\mapsto 9\mapsto 2\mapsto 2),(6\mapsto 9\mapsto 3\mapsto 3),(6\mapsto 9\mapsto 4\mapsto 4),(6\mapsto 9\mapsto 5\mapsto 5),(6\mapsto 9\mapsto 6\mapsto 6),(6\mapsto 9\mapsto 7\mapsto 7),(6\mapsto 9\mapsto 8\mapsto 8),(6\mapsto 9\mapsto 9\mapsto 9),(7\mapsto 8\mapsto 1\mapsto 1),(7\mapsto 8\mapsto 2\mapsto 2),(7\mapsto 8\mapsto 3\mapsto 3),(7\mapsto 8\mapsto 4\mapsto 4),(7\mapsto 8\mapsto 5\mapsto 5),(7\mapsto 8\mapsto 6\mapsto 6),(7\mapsto 8\mapsto 7\mapsto 7),(7\mapsto 8\mapsto 8\mapsto 8),(7\mapsto 8\mapsto 9\mapsto 9),(7\mapsto 9\mapsto 1\mapsto 1),(7\mapsto 9\mapsto 2\mapsto 2),(7\mapsto 9\mapsto 3\mapsto 3),(7\mapsto 9\mapsto 4\mapsto 4),(7\mapsto 9\mapsto 5\mapsto 5),(7\mapsto 9\mapsto 6\mapsto 6),(7\mapsto 9\mapsto 7\mapsto 7),(7\mapsto 9\mapsto 8\mapsto 8),(7\mapsto 9\mapsto 9\mapsto 9),(8\mapsto 9\mapsto 1\mapsto 1),(8\mapsto 9\mapsto 2\mapsto 2),(8\mapsto 9\mapsto 3\mapsto 3),(8\mapsto 9\mapsto 4\mapsto 4),(8\mapsto 9\mapsto 5\mapsto 5),(8\mapsto 9\mapsto 6\mapsto 6),(8\mapsto 9\mapsto 7\mapsto 7),(8\mapsto 9\mapsto 8\mapsto 8),(8\mapsto 9\mapsto 9\mapsto 9)\}$
* $\mathit{SUBSQ} = \{\{1,2,3\},\{4,5,6\},\{7,8,9\}\}$
TRUE
Solution:
Diff2 = {(1↦1↦1↦2),(1↦1↦1↦3),(1↦1↦1↦4),(1↦1↦1↦5),(1↦1↦1↦6),(1↦1↦1↦7),(1↦1↦1↦8),(1↦1↦1↦9),(1↦1↦2↦3),(1↦1↦2↦4),(1↦1↦2↦5),(1↦1↦2↦6),(1↦1↦2↦7),(1↦1↦2↦8),(1↦1↦2↦9),(1↦1↦3↦4),(1↦1↦3↦5),(1↦1↦3↦6),(1↦1↦3↦7),(1↦1↦3↦8),(1↦1↦3↦9),(1↦1↦4↦5),(1↦1↦4↦6),(1↦1↦4↦7),(1↦1↦4↦8),(1↦1↦4↦9),(1↦1↦5↦6),(1↦1↦5↦7),(1↦1↦5↦8),(1↦1↦5↦9),(1↦1↦6↦7),(1↦1↦6↦8),(1↦1↦6↦9),(1↦1↦7↦8),(1↦1↦7↦9),(1↦1↦8↦9),(2↦2↦1↦2),(2↦2↦1↦3),(2↦2↦1↦4),(2↦2↦1↦5),(2↦2↦1↦6),(2↦2↦1↦7),(2↦2↦1↦8),(2↦2↦1↦9),(2↦2↦2↦3),(2↦2↦2↦4),(2↦2↦2↦5),(2↦2↦2↦6),(2↦2↦2↦7),(2↦2↦2↦8),(2↦2↦2↦9),(2↦2↦3↦4),(2↦2↦3↦5),(2↦2↦3↦6),(2↦2↦3↦7),(2↦2↦3↦8),(2↦2↦3↦9),(2↦2↦4↦5),(2↦2↦4↦6),(2↦2↦4↦7),(2↦2↦4↦8),(2↦2↦4↦9),(2↦2↦5↦6),(2↦2↦5↦7),(2↦2↦5↦8),(2↦2↦5↦9),(2↦2↦6↦7),(2↦2↦6↦8),(2↦2↦6↦9),(2↦2↦7↦8),(2↦2↦7↦9),(2↦2↦8↦9),(3↦3↦1↦2),(3↦3↦1↦3),(3↦3↦1↦4),(3↦3↦1↦5),(3↦3↦1↦6),(3↦3↦1↦7),(3↦3↦1↦8),(3↦3↦1↦9),(3↦3↦2↦3),(3↦3↦2↦4),(3↦3↦2↦5),(3↦3↦2↦6),(3↦3↦2↦7),(3↦3↦2↦8),(3↦3↦2↦9),(3↦3↦3↦4),(3↦3↦3↦5),(3↦3↦3↦6),(3↦3↦3↦7),(3↦3↦3↦8),(3↦3↦3↦9),(3↦3↦4↦5),(3↦3↦4↦6),(3↦3↦4↦7),(3↦3↦4↦8),(3↦3↦4↦9),(3↦3↦5↦6),(3↦3↦5↦7),(3↦3↦5↦8),(3↦3↦5↦9),(3↦3↦6↦7),(3↦3↦6↦8),(3↦3↦6↦9),(3↦3↦7↦8),(3↦3↦7↦9),(3↦3↦8↦9),(4↦4↦1↦2),(4↦4↦1↦3),(4↦4↦1↦4),(4↦4↦1↦5),(4↦4↦1↦6),(4↦4↦1↦7),(4↦4↦1↦8),(4↦4↦1↦9),(4↦4↦2↦3),(4↦4↦2↦4),(4↦4↦2↦5),(4↦4↦2↦6),(4↦4↦2↦7),(4↦4↦2↦8),(4↦4↦2↦9),(4↦4↦3↦4),(4↦4↦3↦5),(4↦4↦3↦6),(4↦4↦3↦7),(4↦4↦3↦8),(4↦4↦3↦9),(4↦4↦4↦5),(4↦4↦4↦6),(4↦4↦4↦7),(4↦4↦4↦8),(4↦4↦4↦9),(4↦4↦5↦6),(4↦4↦5↦7),(4↦4↦5↦8),(4↦4↦5↦9),(4↦4↦6↦7),(4↦4↦6↦8),(4↦4↦6↦9),(4↦4↦7↦8),(4↦4↦7↦9),(4↦4↦8↦9),(5↦5↦1↦2),(5↦5↦1↦3),(5↦5↦1↦4),(5↦5↦1↦5),(5↦5↦1↦6),(5↦5↦1↦7),(5↦5↦1↦8),(5↦5↦1↦9),(5↦5↦2↦3),(5↦5↦2↦4),(5↦5↦2↦5),(5↦5↦2↦6),(5↦5↦2↦7),(5↦5↦2↦8),(5↦5↦2↦9),(5↦5↦3↦4),(5↦5↦3↦5),(5↦5↦3↦6),(5↦5↦3↦7),(5↦5↦3↦8),(5↦5↦3↦9),(5↦5↦4↦5),(5↦5↦4↦6),(5↦5↦4↦7),(5↦5↦4↦8),(5↦5↦4↦9),(5↦5↦5↦6),(5↦5↦5↦7),(5↦5↦5↦8),(5↦5↦5↦9),(5↦5↦6↦7),(5↦5↦6↦8),(5↦5↦6↦9),(5↦5↦7↦8),(5↦5↦7↦9),(5↦5↦8↦9),(6↦6↦1↦2),(6↦6↦1↦3),(6↦6↦1↦4),(6↦6↦1↦5),(6↦6↦1↦6),(6↦6↦1↦7),(6↦6↦1↦8),(6↦6↦1↦9),(6↦6↦2↦3),(6↦6↦2↦4),(6↦6↦2↦5),(6↦6↦2↦6),(6↦6↦2↦7),(6↦6↦2↦8),(6↦6↦2↦9),(6↦6↦3↦4),(6↦6↦3↦5),(6↦6↦3↦6),(6↦6↦3↦7),(6↦6↦3↦8),(6↦6↦3↦9),(6↦6↦4↦5),(6↦6↦4↦6),(6↦6↦4↦7),(6↦6↦4↦8),(6↦6↦4↦9),(6↦6↦5↦6),(6↦6↦5↦7),(6↦6↦5↦8),(6↦6↦5↦9),(6↦6↦6↦7),(6↦6↦6↦8),(6↦6↦6↦9),(6↦6↦7↦8),(6↦6↦7↦9),(6↦6↦8↦9),(7↦7↦1↦2),(7↦7↦1↦3),(7↦7↦1↦4),(7↦7↦1↦5),(7↦7↦1↦6),(7↦7↦1↦7),(7↦7↦1↦8),(7↦7↦1↦9),(7↦7↦2↦3),(7↦7↦2↦4),(7↦7↦2↦5),(7↦7↦2↦6),(7↦7↦2↦7),(7↦7↦2↦8),(7↦7↦2↦9),(7↦7↦3↦4),(7↦7↦3↦5),(7↦7↦3↦6),(7↦7↦3↦7),(7↦7↦3↦8),(7↦7↦3↦9),(7↦7↦4↦5),(7↦7↦4↦6),(7↦7↦4↦7),(7↦7↦4↦8),(7↦7↦4↦9),(7↦7↦5↦6),(7↦7↦5↦7),(7↦7↦5↦8),(7↦7↦5↦9),(7↦7↦6↦7),(7↦7↦6↦8),(7↦7↦6↦9),(7↦7↦7↦8),(7↦7↦7↦9),(7↦7↦8↦9),(8↦8↦1↦2),(8↦8↦1↦3),(8↦8↦1↦4),(8↦8↦1↦5),(8↦8↦1↦6),(8↦8↦1↦7),(8↦8↦1↦8),(8↦8↦1↦9),(8↦8↦2↦3),(8↦8↦2↦4),(8↦8↦2↦5),(8↦8↦2↦6),(8↦8↦2↦7),(8↦8↦2↦8),(8↦8↦2↦9),(8↦8↦3↦4),(8↦8↦3↦5),(8↦8↦3↦6),(8↦8↦3↦7),(8↦8↦3↦8),(8↦8↦3↦9),(8↦8↦4↦5),(8↦8↦4↦6),(8↦8↦4↦7),(8↦8↦4↦8),(8↦8↦4↦9),(8↦8↦5↦6),(8↦8↦5↦7),(8↦8↦5↦8),(8↦8↦5↦9),(8↦8↦6↦7),(8↦8↦6↦8),(8↦8↦6↦9),(8↦8↦7↦8),(8↦8↦7↦9),(8↦8↦8↦9),(9↦9↦1↦2),(9↦9↦1↦3),(9↦9↦1↦4),(9↦9↦1↦5),(9↦9↦1↦6),(9↦9↦1↦7),(9↦9↦1↦8),(9↦9↦1↦9),(9↦9↦2↦3),(9↦9↦2↦4),(9↦9↦2↦5),(9↦9↦2↦6),(9↦9↦2↦7),(9↦9↦2↦8),(9↦9↦2↦9),(9↦9↦3↦4),(9↦9↦3↦5),(9↦9↦3↦6),(9↦9↦3↦7),(9↦9↦3↦8),(9↦9↦3↦9),(9↦9↦4↦5),(9↦9↦4↦6),(9↦9↦4↦7),(9↦9↦4↦8),(9↦9↦4↦9),(9↦9↦5↦6),(9↦9↦5↦7),(9↦9↦5↦8),(9↦9↦5↦9),(9↦9↦6↦7),(9↦9↦6↦8),(9↦9↦6↦9),(9↦9↦7↦8),(9↦9↦7↦9),(9↦9↦8↦9)}
Board = {(1↦{(1↦2),(2↦5),(3↦4),(4↦1),(5↦3),(6↦6),(7↦7),(8↦8),(9↦9)}),(2↦{(1↦1),(2↦4),(3↦2),(4↦3),(5↦6),(6↦5),(7↦9),(8↦7),(9↦8)}),(3↦{(1↦4),(2↦9),(3↦3),(4↦2),(5↦1),(6↦8),(7↦5),(8↦6),(9↦7)}),(4↦{(1↦3),(2↦1),(3↦8),(4↦7),(5↦9),(6↦2),(7↦4),(8↦5),(9↦6)}),(5↦{(1↦6),(2↦3),(3↦9),(4↦8),(5↦7),(6↦1),(7↦2),(8↦4),(9↦5)}),(6↦{(1↦5),(2↦2),(3↦1),(4↦9),(5↦8),(6↦7),(7↦6),(8↦3),(9↦4)}),(7↦{(1↦7),(2↦6),(3↦5),(4↦4),(5↦2),(6↦9),(7↦8),(8↦1),(9↦3)}),(8↦{(1↦8),(2↦7),(3↦6),(4↦5),(5↦4),(6↦3),(7↦1),(8↦9),(9↦2)}),(9↦{(1↦9),(2↦8),(3↦7),(4↦6),(5↦5),(6↦4),(7↦3),(8↦2),(9↦1)})}
DOM = {1,2,3,4,5,6,7,8,9}
Diff1 = {(1↦2↦1↦1),(1↦2↦2↦2),(1↦2↦3↦3),(1↦2↦4↦4),(1↦2↦5↦5),(1↦2↦6↦6),(1↦2↦7↦7),(1↦2↦8↦8),(1↦2↦9↦9),(1↦3↦1↦1),(1↦3↦2↦2),(1↦3↦3↦3),(1↦3↦4↦4),(1↦3↦5↦5),(1↦3↦6↦6),(1↦3↦7↦7),(1↦3↦8↦8),(1↦3↦9↦9),(1↦4↦1↦1),(1↦4↦2↦2),(1↦4↦3↦3),(1↦4↦4↦4),(1↦4↦5↦5),(1↦4↦6↦6),(1↦4↦7↦7),(1↦4↦8↦8),(1↦4↦9↦9),(1↦5↦1↦1),(1↦5↦2↦2),(1↦5↦3↦3),(1↦5↦4↦4),(1↦5↦5↦5),(1↦5↦6↦6),(1↦5↦7↦7),(1↦5↦8↦8),(1↦5↦9↦9),(1↦6↦1↦1),(1↦6↦2↦2),(1↦6↦3↦3),(1↦6↦4↦4),(1↦6↦5↦5),(1↦6↦6↦6),(1↦6↦7↦7),(1↦6↦8↦8),(1↦6↦9↦9),(1↦7↦1↦1),(1↦7↦2↦2),(1↦7↦3↦3),(1↦7↦4↦4),(1↦7↦5↦5),(1↦7↦6↦6),(1↦7↦7↦7),(1↦7↦8↦8),(1↦7↦9↦9),(1↦8↦1↦1),(1↦8↦2↦2),(1↦8↦3↦3),(1↦8↦4↦4),(1↦8↦5↦5),(1↦8↦6↦6),(1↦8↦7↦7),(1↦8↦8↦8),(1↦8↦9↦9),(1↦9↦1↦1),(1↦9↦2↦2),(1↦9↦3↦3),(1↦9↦4↦4),(1↦9↦5↦5),(1↦9↦6↦6),(1↦9↦7↦7),(1↦9↦8↦8),(1↦9↦9↦9),(2↦3↦1↦1),(2↦3↦2↦2),(2↦3↦3↦3),(2↦3↦4↦4),(2↦3↦5↦5),(2↦3↦6↦6),(2↦3↦7↦7),(2↦3↦8↦8),(2↦3↦9↦9),(2↦4↦1↦1),(2↦4↦2↦2),(2↦4↦3↦3),(2↦4↦4↦4),(2↦4↦5↦5),(2↦4↦6↦6),(2↦4↦7↦7),(2↦4↦8↦8),(2↦4↦9↦9),(2↦5↦1↦1),(2↦5↦2↦2),(2↦5↦3↦3),(2↦5↦4↦4),(2↦5↦5↦5),(2↦5↦6↦6),(2↦5↦7↦7),(2↦5↦8↦8),(2↦5↦9↦9),(2↦6↦1↦1),(2↦6↦2↦2),(2↦6↦3↦3),(2↦6↦4↦4),(2↦6↦5↦5),(2↦6↦6↦6),(2↦6↦7↦7),(2↦6↦8↦8),(2↦6↦9↦9),(2↦7↦1↦1),(2↦7↦2↦2),(2↦7↦3↦3),(2↦7↦4↦4),(2↦7↦5↦5),(2↦7↦6↦6),(2↦7↦7↦7),(2↦7↦8↦8),(2↦7↦9↦9),(2↦8↦1↦1),(2↦8↦2↦2),(2↦8↦3↦3),(2↦8↦4↦4),(2↦8↦5↦5),(2↦8↦6↦6),(2↦8↦7↦7),(2↦8↦8↦8),(2↦8↦9↦9),(2↦9↦1↦1),(2↦9↦2↦2),(2↦9↦3↦3),(2↦9↦4↦4),(2↦9↦5↦5),(2↦9↦6↦6),(2↦9↦7↦7),(2↦9↦8↦8),(2↦9↦9↦9),(3↦4↦1↦1),(3↦4↦2↦2),(3↦4↦3↦3),(3↦4↦4↦4),(3↦4↦5↦5),(3↦4↦6↦6),(3↦4↦7↦7),(3↦4↦8↦8),(3↦4↦9↦9),(3↦5↦1↦1),(3↦5↦2↦2),(3↦5↦3↦3),(3↦5↦4↦4),(3↦5↦5↦5),(3↦5↦6↦6),(3↦5↦7↦7),(3↦5↦8↦8),(3↦5↦9↦9),(3↦6↦1↦1),(3↦6↦2↦2),(3↦6↦3↦3),(3↦6↦4↦4),(3↦6↦5↦5),(3↦6↦6↦6),(3↦6↦7↦7),(3↦6↦8↦8),(3↦6↦9↦9),(3↦7↦1↦1),(3↦7↦2↦2),(3↦7↦3↦3),(3↦7↦4↦4),(3↦7↦5↦5),(3↦7↦6↦6),(3↦7↦7↦7),(3↦7↦8↦8),(3↦7↦9↦9),(3↦8↦1↦1),(3↦8↦2↦2),(3↦8↦3↦3),(3↦8↦4↦4),(3↦8↦5↦5),(3↦8↦6↦6),(3↦8↦7↦7),(3↦8↦8↦8),(3↦8↦9↦9),(3↦9↦1↦1),(3↦9↦2↦2),(3↦9↦3↦3),(3↦9↦4↦4),(3↦9↦5↦5),(3↦9↦6↦6),(3↦9↦7↦7),(3↦9↦8↦8),(3↦9↦9↦9),(4↦5↦1↦1),(4↦5↦2↦2),(4↦5↦3↦3),(4↦5↦4↦4),(4↦5↦5↦5),(4↦5↦6↦6),(4↦5↦7↦7),(4↦5↦8↦8),(4↦5↦9↦9),(4↦6↦1↦1),(4↦6↦2↦2),(4↦6↦3↦3),(4↦6↦4↦4),(4↦6↦5↦5),(4↦6↦6↦6),(4↦6↦7↦7),(4↦6↦8↦8),(4↦6↦9↦9),(4↦7↦1↦1),(4↦7↦2↦2),(4↦7↦3↦3),(4↦7↦4↦4),(4↦7↦5↦5),(4↦7↦6↦6),(4↦7↦7↦7),(4↦7↦8↦8),(4↦7↦9↦9),(4↦8↦1↦1),(4↦8↦2↦2),(4↦8↦3↦3),(4↦8↦4↦4),(4↦8↦5↦5),(4↦8↦6↦6),(4↦8↦7↦7),(4↦8↦8↦8),(4↦8↦9↦9),(4↦9↦1↦1),(4↦9↦2↦2),(4↦9↦3↦3),(4↦9↦4↦4),(4↦9↦5↦5),(4↦9↦6↦6),(4↦9↦7↦7),(4↦9↦8↦8),(4↦9↦9↦9),(5↦6↦1↦1),(5↦6↦2↦2),(5↦6↦3↦3),(5↦6↦4↦4),(5↦6↦5↦5),(5↦6↦6↦6),(5↦6↦7↦7),(5↦6↦8↦8),(5↦6↦9↦9),(5↦7↦1↦1),(5↦7↦2↦2),(5↦7↦3↦3),(5↦7↦4↦4),(5↦7↦5↦5),(5↦7↦6↦6),(5↦7↦7↦7),(5↦7↦8↦8),(5↦7↦9↦9),(5↦8↦1↦1),(5↦8↦2↦2),(5↦8↦3↦3),(5↦8↦4↦4),(5↦8↦5↦5),(5↦8↦6↦6),(5↦8↦7↦7),(5↦8↦8↦8),(5↦8↦9↦9),(5↦9↦1↦1),(5↦9↦2↦2),(5↦9↦3↦3),(5↦9↦4↦4),(5↦9↦5↦5),(5↦9↦6↦6),(5↦9↦7↦7),(5↦9↦8↦8),(5↦9↦9↦9),(6↦7↦1↦1),(6↦7↦2↦2),(6↦7↦3↦3),(6↦7↦4↦4),(6↦7↦5↦5),(6↦7↦6↦6),(6↦7↦7↦7),(6↦7↦8↦8),(6↦7↦9↦9),(6↦8↦1↦1),(6↦8↦2↦2),(6↦8↦3↦3),(6↦8↦4↦4),(6↦8↦5↦5),(6↦8↦6↦6),(6↦8↦7↦7),(6↦8↦8↦8),(6↦8↦9↦9),(6↦9↦1↦1),(6↦9↦2↦2),(6↦9↦3↦3),(6↦9↦4↦4),(6↦9↦5↦5),(6↦9↦6↦6),(6↦9↦7↦7),(6↦9↦8↦8),(6↦9↦9↦9),(7↦8↦1↦1),(7↦8↦2↦2),(7↦8↦3↦3),(7↦8↦4↦4),(7↦8↦5↦5),(7↦8↦6↦6),(7↦8↦7↦7),(7↦8↦8↦8),(7↦8↦9↦9),(7↦9↦1↦1),(7↦9↦2↦2),(7↦9↦3↦3),(7↦9↦4↦4),(7↦9↦5↦5),(7↦9↦6↦6),(7↦9↦7↦7),(7↦9↦8↦8),(7↦9↦9↦9),(8↦9↦1↦1),(8↦9↦2↦2),(8↦9↦3↦3),(8↦9↦4↦4),(8↦9↦5↦5),(8↦9↦6↦6),(8↦9↦7↦7),(8↦9↦8↦8),(8↦9↦9↦9)}
SUBSQ = {{1,2,3},{4,5,6},{7,8,9}}
%% Cell type:markdown id: tags:
Now, we will try and complete the constraints and put pairs of co-ordinates within each sub-square into the variable `Diff3`, and computing the union of `Diff1`, `Diff2` and `Diff3`:
%% Cell type:code id: tags:
``` prob
:let Diff3 {x1,x2,y1,y2|#(s1,s2).(s1:SUBSQ & s2:SUBSQ & x1:s1 & x2:s1 & x1>=x2 & (x1=x2 => y1>y2) & y1:s2 & y2:s2 & (x1,y1) /= (x2,y2))}
```
%% Output
$\{(1\mapsto 1\mapsto 2\mapsto 1),(1\mapsto 1\mapsto 3\mapsto 1),(1\mapsto 1\mapsto 3\mapsto 2),(1\mapsto 1\mapsto 5\mapsto 4),(1\mapsto 1\mapsto 6\mapsto 4),(1\mapsto 1\mapsto 6\mapsto 5),(1\mapsto 1\mapsto 8\mapsto 7),(1\mapsto 1\mapsto 9\mapsto 7),(1\mapsto 1\mapsto 9\mapsto 8),(2\mapsto 1\mapsto 1\mapsto 1),(2\mapsto 1\mapsto 1\mapsto 2),(2\mapsto 1\mapsto 1\mapsto 3),(2\mapsto 1\mapsto 2\mapsto 1),(2\mapsto 1\mapsto 2\mapsto 2),(2\mapsto 1\mapsto 2\mapsto 3),(2\mapsto 1\mapsto 3\mapsto 1),(2\mapsto 1\mapsto 3\mapsto 2),(2\mapsto 1\mapsto 3\mapsto 3),(2\mapsto 1\mapsto 4\mapsto 4),(2\mapsto 1\mapsto 4\mapsto 5),(2\mapsto 1\mapsto 4\mapsto 6),(2\mapsto 1\mapsto 5\mapsto 4),(2\mapsto 1\mapsto 5\mapsto 5),(2\mapsto 1\mapsto 5\mapsto 6),(2\mapsto 1\mapsto 6\mapsto 4),(2\mapsto 1\mapsto 6\mapsto 5),(2\mapsto 1\mapsto 6\mapsto 6),(2\mapsto 1\mapsto 7\mapsto 7),(2\mapsto 1\mapsto 7\mapsto 8),(2\mapsto 1\mapsto 7\mapsto 9),(2\mapsto 1\mapsto 8\mapsto 7),(2\mapsto 1\mapsto 8\mapsto 8),(2\mapsto 1\mapsto 8\mapsto 9),(2\mapsto 1\mapsto 9\mapsto 7),(2\mapsto 1\mapsto 9\mapsto 8),(2\mapsto 1\mapsto 9\mapsto 9),(2\mapsto 2\mapsto 2\mapsto 1),(2\mapsto 2\mapsto 3\mapsto 1),(2\mapsto 2\mapsto 3\mapsto 2),(2\mapsto 2\mapsto 5\mapsto 4),(2\mapsto 2\mapsto 6\mapsto 4),(2\mapsto 2\mapsto 6\mapsto 5),(2\mapsto 2\mapsto 8\mapsto 7),(2\mapsto 2\mapsto 9\mapsto 7),(2\mapsto 2\mapsto 9\mapsto 8),(3\mapsto 1\mapsto 1\mapsto 1),(3\mapsto 1\mapsto 1\mapsto 2),(3\mapsto 1\mapsto 1\mapsto 3),(3\mapsto 1\mapsto 2\mapsto 1),(3\mapsto 1\mapsto 2\mapsto 2),(3\mapsto 1\mapsto 2\mapsto 3),(3\mapsto 1\mapsto 3\mapsto 1),(3\mapsto 1\mapsto 3\mapsto 2),(3\mapsto 1\mapsto 3\mapsto 3),(3\mapsto 1\mapsto 4\mapsto 4),(3\mapsto 1\mapsto 4\mapsto 5),(3\mapsto 1\mapsto 4\mapsto 6),(3\mapsto 1\mapsto 5\mapsto 4),(3\mapsto 1\mapsto 5\mapsto 5),(3\mapsto 1\mapsto 5\mapsto 6),(3\mapsto 1\mapsto 6\mapsto 4),(3\mapsto 1\mapsto 6\mapsto 5),(3\mapsto 1\mapsto 6\mapsto 6),(3\mapsto 1\mapsto 7\mapsto 7),(3\mapsto 1\mapsto 7\mapsto 8),(3\mapsto 1\mapsto 7\mapsto 9),(3\mapsto 1\mapsto 8\mapsto 7),(3\mapsto 1\mapsto 8\mapsto 8),(3\mapsto 1\mapsto 8\mapsto 9),(3\mapsto 1\mapsto 9\mapsto 7),(3\mapsto 1\mapsto 9\mapsto 8),(3\mapsto 1\mapsto 9\mapsto 9),(3\mapsto 2\mapsto 1\mapsto 1),(3\mapsto 2\mapsto 1\mapsto 2),(3\mapsto 2\mapsto 1\mapsto 3),(3\mapsto 2\mapsto 2\mapsto 1),(3\mapsto 2\mapsto 2\mapsto 2),(3\mapsto 2\mapsto 2\mapsto 3),(3\mapsto 2\mapsto 3\mapsto 1),(3\mapsto 2\mapsto 3\mapsto 2),(3\mapsto 2\mapsto 3\mapsto 3),(3\mapsto 2\mapsto 4\mapsto 4),(3\mapsto 2\mapsto 4\mapsto 5),(3\mapsto 2\mapsto 4\mapsto 6),(3\mapsto 2\mapsto 5\mapsto 4),(3\mapsto 2\mapsto 5\mapsto 5),(3\mapsto 2\mapsto 5\mapsto 6),(3\mapsto 2\mapsto 6\mapsto 4),(3\mapsto 2\mapsto 6\mapsto 5),(3\mapsto 2\mapsto 6\mapsto 6),(3\mapsto 2\mapsto 7\mapsto 7),(3\mapsto 2\mapsto 7\mapsto 8),(3\mapsto 2\mapsto 7\mapsto 9),(3\mapsto 2\mapsto 8\mapsto 7),(3\mapsto 2\mapsto 8\mapsto 8),(3\mapsto 2\mapsto 8\mapsto 9),(3\mapsto 2\mapsto 9\mapsto 7),(3\mapsto 2\mapsto 9\mapsto 8),(3\mapsto 2\mapsto 9\mapsto 9),(3\mapsto 3\mapsto 2\mapsto 1),(3\mapsto 3\mapsto 3\mapsto 1),(3\mapsto 3\mapsto 3\mapsto 2),(3\mapsto 3\mapsto 5\mapsto 4),(3\mapsto 3\mapsto 6\mapsto 4),(3\mapsto 3\mapsto 6\mapsto 5),(3\mapsto 3\mapsto 8\mapsto 7),(3\mapsto 3\mapsto 9\mapsto 7),(3\mapsto 3\mapsto 9\mapsto 8),(4\mapsto 4\mapsto 2\mapsto 1),(4\mapsto 4\mapsto 3\mapsto 1),(4\mapsto 4\mapsto 3\mapsto 2),(4\mapsto 4\mapsto 5\mapsto 4),(4\mapsto 4\mapsto 6\mapsto 4),(4\mapsto 4\mapsto 6\mapsto 5),(4\mapsto 4\mapsto 8\mapsto 7),(4\mapsto 4\mapsto 9\mapsto 7),(4\mapsto 4\mapsto 9\mapsto 8),(5\mapsto 4\mapsto 1\mapsto 1),(5\mapsto 4\mapsto 1\mapsto 2),(5\mapsto 4\mapsto 1\mapsto 3),(5\mapsto 4\mapsto 2\mapsto 1),(5\mapsto 4\mapsto 2\mapsto 2),(5\mapsto 4\mapsto 2\mapsto 3),(5\mapsto 4\mapsto 3\mapsto 1),(5\mapsto 4\mapsto 3\mapsto 2),(5\mapsto 4\mapsto 3\mapsto 3),(5\mapsto 4\mapsto 4\mapsto 4),(5\mapsto 4\mapsto 4\mapsto 5),(5\mapsto 4\mapsto 4\mapsto 6),(5\mapsto 4\mapsto 5\mapsto 4),(5\mapsto 4\mapsto 5\mapsto 5),(5\mapsto 4\mapsto 5\mapsto 6),(5\mapsto 4\mapsto 6\mapsto 4),(5\mapsto 4\mapsto 6\mapsto 5),(5\mapsto 4\mapsto 6\mapsto 6),(5\mapsto 4\mapsto 7\mapsto 7),(5\mapsto 4\mapsto 7\mapsto 8),(5\mapsto 4\mapsto 7\mapsto 9),(5\mapsto 4\mapsto 8\mapsto 7),(5\mapsto 4\mapsto 8\mapsto 8),(5\mapsto 4\mapsto 8\mapsto 9),(5\mapsto 4\mapsto 9\mapsto 7),(5\mapsto 4\mapsto 9\mapsto 8),(5\mapsto 4\mapsto 9\mapsto 9),(5\mapsto 5\mapsto 2\mapsto 1),(5\mapsto 5\mapsto 3\mapsto 1),(5\mapsto 5\mapsto 3\mapsto 2),(5\mapsto 5\mapsto 5\mapsto 4),(5\mapsto 5\mapsto 6\mapsto 4),(5\mapsto 5\mapsto 6\mapsto 5),(5\mapsto 5\mapsto 8\mapsto 7),(5\mapsto 5\mapsto 9\mapsto 7),(5\mapsto 5\mapsto 9\mapsto 8),(6\mapsto 4\mapsto 1\mapsto 1),(6\mapsto 4\mapsto 1\mapsto 2),(6\mapsto 4\mapsto 1\mapsto 3),(6\mapsto 4\mapsto 2\mapsto 1),(6\mapsto 4\mapsto 2\mapsto 2),(6\mapsto 4\mapsto 2\mapsto 3),(6\mapsto 4\mapsto 3\mapsto 1),(6\mapsto 4\mapsto 3\mapsto 2),(6\mapsto 4\mapsto 3\mapsto 3),(6\mapsto 4\mapsto 4\mapsto 4),(6\mapsto 4\mapsto 4\mapsto 5),(6\mapsto 4\mapsto 4\mapsto 6),(6\mapsto 4\mapsto 5\mapsto 4),(6\mapsto 4\mapsto 5\mapsto 5),(6\mapsto 4\mapsto 5\mapsto 6),(6\mapsto 4\mapsto 6\mapsto 4),(6\mapsto 4\mapsto 6\mapsto 5),(6\mapsto 4\mapsto 6\mapsto 6),(6\mapsto 4\mapsto 7\mapsto 7),(6\mapsto 4\mapsto 7\mapsto 8),(6\mapsto 4\mapsto 7\mapsto 9),(6\mapsto 4\mapsto 8\mapsto 7),(6\mapsto 4\mapsto 8\mapsto 8),(6\mapsto 4\mapsto 8\mapsto 9),(6\mapsto 4\mapsto 9\mapsto 7),(6\mapsto 4\mapsto 9\mapsto 8),(6\mapsto 4\mapsto 9\mapsto 9),(6\mapsto 5\mapsto 1\mapsto 1),(6\mapsto 5\mapsto 1\mapsto 2),(6\mapsto 5\mapsto 1\mapsto 3),(6\mapsto 5\mapsto 2\mapsto 1),(6\mapsto 5\mapsto 2\mapsto 2),(6\mapsto 5\mapsto 2\mapsto 3),(6\mapsto 5\mapsto 3\mapsto 1),(6\mapsto 5\mapsto 3\mapsto 2),(6\mapsto 5\mapsto 3\mapsto 3),(6\mapsto 5\mapsto 4\mapsto 4),(6\mapsto 5\mapsto 4\mapsto 5),(6\mapsto 5\mapsto 4\mapsto 6),(6\mapsto 5\mapsto 5\mapsto 4),(6\mapsto 5\mapsto 5\mapsto 5),(6\mapsto 5\mapsto 5\mapsto 6),(6\mapsto 5\mapsto 6\mapsto 4),(6\mapsto 5\mapsto 6\mapsto 5),(6\mapsto 5\mapsto 6\mapsto 6),(6\mapsto 5\mapsto 7\mapsto 7),(6\mapsto 5\mapsto 7\mapsto 8),(6\mapsto 5\mapsto 7\mapsto 9),(6\mapsto 5\mapsto 8\mapsto 7),(6\mapsto 5\mapsto 8\mapsto 8),(6\mapsto 5\mapsto 8\mapsto 9),(6\mapsto 5\mapsto 9\mapsto 7),(6\mapsto 5\mapsto 9\mapsto 8),(6\mapsto 5\mapsto 9\mapsto 9),(6\mapsto 6\mapsto 2\mapsto 1),(6\mapsto 6\mapsto 3\mapsto 1),(6\mapsto 6\mapsto 3\mapsto 2),(6\mapsto 6\mapsto 5\mapsto 4),(6\mapsto 6\mapsto 6\mapsto 4),(6\mapsto 6\mapsto 6\mapsto 5),(6\mapsto 6\mapsto 8\mapsto 7),(6\mapsto 6\mapsto 9\mapsto 7),(6\mapsto 6\mapsto 9\mapsto 8),(7\mapsto 7\mapsto 2\mapsto 1),(7\mapsto 7\mapsto 3\mapsto 1),(7\mapsto 7\mapsto 3\mapsto 2),(7\mapsto 7\mapsto 5\mapsto 4),(7\mapsto 7\mapsto 6\mapsto 4),(7\mapsto 7\mapsto 6\mapsto 5),(7\mapsto 7\mapsto 8\mapsto 7),(7\mapsto 7\mapsto 9\mapsto 7),(7\mapsto 7\mapsto 9\mapsto 8),(8\mapsto 7\mapsto 1\mapsto 1),(8\mapsto 7\mapsto 1\mapsto 2),(8\mapsto 7\mapsto 1\mapsto 3),(8\mapsto 7\mapsto 2\mapsto 1),(8\mapsto 7\mapsto 2\mapsto 2),(8\mapsto 7\mapsto 2\mapsto 3),(8\mapsto 7\mapsto 3\mapsto 1),(8\mapsto 7\mapsto 3\mapsto 2),(8\mapsto 7\mapsto 3\mapsto 3),(8\mapsto 7\mapsto 4\mapsto 4),(8\mapsto 7\mapsto 4\mapsto 5),(8\mapsto 7\mapsto 4\mapsto 6),(8\mapsto 7\mapsto 5\mapsto 4),(8\mapsto 7\mapsto 5\mapsto 5),(8\mapsto 7\mapsto 5\mapsto 6),(8\mapsto 7\mapsto 6\mapsto 4),(8\mapsto 7\mapsto 6\mapsto 5),(8\mapsto 7\mapsto 6\mapsto 6),(8\mapsto 7\mapsto 7\mapsto 7),(8\mapsto 7\mapsto 7\mapsto 8),(8\mapsto 7\mapsto 7\mapsto 9),(8\mapsto 7\mapsto 8\mapsto 7),(8\mapsto 7\mapsto 8\mapsto 8),(8\mapsto 7\mapsto 8\mapsto 9),(8\mapsto 7\mapsto 9\mapsto 7),(8\mapsto 7\mapsto 9\mapsto 8),(8\mapsto 7\mapsto 9\mapsto 9),(8\mapsto 8\mapsto 2\mapsto 1),(8\mapsto 8\mapsto 3\mapsto 1),(8\mapsto 8\mapsto 3\mapsto 2),(8\mapsto 8\mapsto 5\mapsto 4),(8\mapsto 8\mapsto 6\mapsto 4),(8\mapsto 8\mapsto 6\mapsto 5),(8\mapsto 8\mapsto 8\mapsto 7),(8\mapsto 8\mapsto 9\mapsto 7),(8\mapsto 8\mapsto 9\mapsto 8),(9\mapsto 7\mapsto 1\mapsto 1),(9\mapsto 7\mapsto 1\mapsto 2),(9\mapsto 7\mapsto 1\mapsto 3),(9\mapsto 7\mapsto 2\mapsto 1),(9\mapsto 7\mapsto 2\mapsto 2),(9\mapsto 7\mapsto 2\mapsto 3),(9\mapsto 7\mapsto 3\mapsto 1),(9\mapsto 7\mapsto 3\mapsto 2),(9\mapsto 7\mapsto 3\mapsto 3),(9\mapsto 7\mapsto 4\mapsto 4),(9\mapsto 7\mapsto 4\mapsto 5),(9\mapsto 7\mapsto 4\mapsto 6),(9\mapsto 7\mapsto 5\mapsto 4),(9\mapsto 7\mapsto 5\mapsto 5),(9\mapsto 7\mapsto 5\mapsto 6),(9\mapsto 7\mapsto 6\mapsto 4),(9\mapsto 7\mapsto 6\mapsto 5),(9\mapsto 7\mapsto 6\mapsto 6),(9\mapsto 7\mapsto 7\mapsto 7),(9\mapsto 7\mapsto 7\mapsto 8),(9\mapsto 7\mapsto 7\mapsto 9),(9\mapsto 7\mapsto 8\mapsto 7),(9\mapsto 7\mapsto 8\mapsto 8),(9\mapsto 7\mapsto 8\mapsto 9),(9\mapsto 7\mapsto 9\mapsto 7),(9\mapsto 7\mapsto 9\mapsto 8),(9\mapsto 7\mapsto 9\mapsto 9),(9\mapsto 8\mapsto 1\mapsto 1),(9\mapsto 8\mapsto 1\mapsto 2),(9\mapsto 8\mapsto 1\mapsto 3),(9\mapsto 8\mapsto 2\mapsto 1),(9\mapsto 8\mapsto 2\mapsto 2),(9\mapsto 8\mapsto 2\mapsto 3),(9\mapsto 8\mapsto 3\mapsto 1),(9\mapsto 8\mapsto 3\mapsto 2),(9\mapsto 8\mapsto 3\mapsto 3),(9\mapsto 8\mapsto 4\mapsto 4),(9\mapsto 8\mapsto 4\mapsto 5),(9\mapsto 8\mapsto 4\mapsto 6),(9\mapsto 8\mapsto 5\mapsto 4),(9\mapsto 8\mapsto 5\mapsto 5),(9\mapsto 8\mapsto 5\mapsto 6),(9\mapsto 8\mapsto 6\mapsto 4),(9\mapsto 8\mapsto 6\mapsto 5),(9\mapsto 8\mapsto 6\mapsto 6),(9\mapsto 8\mapsto 7\mapsto 7),(9\mapsto 8\mapsto 7\mapsto 8),(9\mapsto 8\mapsto 7\mapsto 9),(9\mapsto 8\mapsto 8\mapsto 7),(9\mapsto 8\mapsto 8\mapsto 8),(9\mapsto 8\mapsto 8\mapsto 9),(9\mapsto 8\mapsto 9\mapsto 7),(9\mapsto 8\mapsto 9\mapsto 8),(9\mapsto 8\mapsto 9\mapsto 9),(9\mapsto 9\mapsto 2\mapsto 1),(9\mapsto 9\mapsto 3\mapsto 1),(9\mapsto 9\mapsto 3\mapsto 2),(9\mapsto 9\mapsto 5\mapsto 4),(9\mapsto 9\mapsto 6\mapsto 4),(9\mapsto 9\mapsto 6\mapsto 5),(9\mapsto 9\mapsto 8\mapsto 7),(9\mapsto 9\mapsto 9\mapsto 7),(9\mapsto 9\mapsto 9\mapsto 8)\}$
{(1↦1↦2↦1),(1↦1↦3↦1),(1↦1↦3↦2),(1↦1↦5↦4),(1↦1↦6↦4),(1↦1↦6↦5),(1↦1↦8↦7),(1↦1↦9↦7),(1↦1↦9↦8),(2↦1↦1↦1),(2↦1↦1↦2),(2↦1↦1↦3),(2↦1↦2↦1),(2↦1↦2↦2),(2↦1↦2↦3),(2↦1↦3↦1),(2↦1↦3↦2),(2↦1↦3↦3),(2↦1↦4↦4),(2↦1↦4↦5),(2↦1↦4↦6),(2↦1↦5↦4),(2↦1↦5↦5),(2↦1↦5↦6),(2↦1↦6↦4),(2↦1↦6↦5),(2↦1↦6↦6),(2↦1↦7↦7),(2↦1↦7↦8),(2↦1↦7↦9),(2↦1↦8↦7),(2↦1↦8↦8),(2↦1↦8↦9),(2↦1↦9↦7),(2↦1↦9↦8),(2↦1↦9↦9),(2↦2↦2↦1),(2↦2↦3↦1),(2↦2↦3↦2),(2↦2↦5↦4),(2↦2↦6↦4),(2↦2↦6↦5),(2↦2↦8↦7),(2↦2↦9↦7),(2↦2↦9↦8),(3↦1↦1↦1),(3↦1↦1↦2),(3↦1↦1↦3),(3↦1↦2↦1),(3↦1↦2↦2),(3↦1↦2↦3),(3↦1↦3↦1),(3↦1↦3↦2),(3↦1↦3↦3),(3↦1↦4↦4),(3↦1↦4↦5),(3↦1↦4↦6),(3↦1↦5↦4),(3↦1↦5↦5),(3↦1↦5↦6),(3↦1↦6↦4),(3↦1↦6↦5),(3↦1↦6↦6),(3↦1↦7↦7),(3↦1↦7↦8),(3↦1↦7↦9),(3↦1↦8↦7),(3↦1↦8↦8),(3↦1↦8↦9),(3↦1↦9↦7),(3↦1↦9↦8),(3↦1↦9↦9),(3↦2↦1↦1),(3↦2↦1↦2),(3↦2↦1↦3),(3↦2↦2↦1),(3↦2↦2↦2),(3↦2↦2↦3),(3↦2↦3↦1),(3↦2↦3↦2),(3↦2↦3↦3),(3↦2↦4↦4),(3↦2↦4↦5),(3↦2↦4↦6),(3↦2↦5↦4),(3↦2↦5↦5),(3↦2↦5↦6),(3↦2↦6↦4),(3↦2↦6↦5),(3↦2↦6↦6),(3↦2↦7↦7),(3↦2↦7↦8),(3↦2↦7↦9),(3↦2↦8↦7),(3↦2↦8↦8),(3↦2↦8↦9),(3↦2↦9↦7),(3↦2↦9↦8),(3↦2↦9↦9),(3↦3↦2↦1),(3↦3↦3↦1),(3↦3↦3↦2),(3↦3↦5↦4),(3↦3↦6↦4),(3↦3↦6↦5),(3↦3↦8↦7),(3↦3↦9↦7),(3↦3↦9↦8),(4↦4↦2↦1),(4↦4↦3↦1),(4↦4↦3↦2),(4↦4↦5↦4),(4↦4↦6↦4),(4↦4↦6↦5),(4↦4↦8↦7),(4↦4↦9↦7),(4↦4↦9↦8),(5↦4↦1↦1),(5↦4↦1↦2),(5↦4↦1↦3),(5↦4↦2↦1),(5↦4↦2↦2),(5↦4↦2↦3),(5↦4↦3↦1),(5↦4↦3↦2),(5↦4↦3↦3),(5↦4↦4↦4),(5↦4↦4↦5),(5↦4↦4↦6),(5↦4↦5↦4),(5↦4↦5↦5),(5↦4↦5↦6),(5↦4↦6↦4),(5↦4↦6↦5),(5↦4↦6↦6),(5↦4↦7↦7),(5↦4↦7↦8),(5↦4↦7↦9),(5↦4↦8↦7),(5↦4↦8↦8),(5↦4↦8↦9),(5↦4↦9↦7),(5↦4↦9↦8),(5↦4↦9↦9),(5↦5↦2↦1),(5↦5↦3↦1),(5↦5↦3↦2),(5↦5↦5↦4),(5↦5↦6↦4),(5↦5↦6↦5),(5↦5↦8↦7),(5↦5↦9↦7),(5↦5↦9↦8),(6↦4↦1↦1),(6↦4↦1↦2),(6↦4↦1↦3),(6↦4↦2↦1),(6↦4↦2↦2),(6↦4↦2↦3),(6↦4↦3↦1),(6↦4↦3↦2),(6↦4↦3↦3),(6↦4↦4↦4),(6↦4↦4↦5),(6↦4↦4↦6),(6↦4↦5↦4),(6↦4↦5↦5),(6↦4↦5↦6),(6↦4↦6↦4),(6↦4↦6↦5),(6↦4↦6↦6),(6↦4↦7↦7),(6↦4↦7↦8),(6↦4↦7↦9),(6↦4↦8↦7),(6↦4↦8↦8),(6↦4↦8↦9),(6↦4↦9↦7),(6↦4↦9↦8),(6↦4↦9↦9),(6↦5↦1↦1),(6↦5↦1↦2),(6↦5↦1↦3),(6↦5↦2↦1),(6↦5↦2↦2),(6↦5↦2↦3),(6↦5↦3↦1),(6↦5↦3↦2),(6↦5↦3↦3),(6↦5↦4↦4),(6↦5↦4↦5),(6↦5↦4↦6),(6↦5↦5↦4),(6↦5↦5↦5),(6↦5↦5↦6),(6↦5↦6↦4),(6↦5↦6↦5),(6↦5↦6↦6),(6↦5↦7↦7),(6↦5↦7↦8),(6↦5↦7↦9),(6↦5↦8↦7),(6↦5↦8↦8),(6↦5↦8↦9),(6↦5↦9↦7),(6↦5↦9↦8),(6↦5↦9↦9),(6↦6↦2↦1),(6↦6↦3↦1),(6↦6↦3↦2),(6↦6↦5↦4),(6↦6↦6↦4),(6↦6↦6↦5),(6↦6↦8↦7),(6↦6↦9↦7),(6↦6↦9↦8),(7↦7↦2↦1),(7↦7↦3↦1),(7↦7↦3↦2),(7↦7↦5↦4),(7↦7↦6↦4),(7↦7↦6↦5),(7↦7↦8↦7),(7↦7↦9↦7),(7↦7↦9↦8),(8↦7↦1↦1),(8↦7↦1↦2),(8↦7↦1↦3),(8↦7↦2↦1),(8↦7↦2↦2),(8↦7↦2↦3),(8↦7↦3↦1),(8↦7↦3↦2),(8↦7↦3↦3),(8↦7↦4↦4),(8↦7↦4↦5),(8↦7↦4↦6),(8↦7↦5↦4),(8↦7↦5↦5),(8↦7↦5↦6),(8↦7↦6↦4),(8↦7↦6↦5),(8↦7↦6↦6),(8↦7↦7↦7),(8↦7↦7↦8),(8↦7↦7↦9),(8↦7↦8↦7),(8↦7↦8↦8),(8↦7↦8↦9),(8↦7↦9↦7),(8↦7↦9↦8),(8↦7↦9↦9),(8↦8↦2↦1),(8↦8↦3↦1),(8↦8↦3↦2),(8↦8↦5↦4),(8↦8↦6↦4),(8↦8↦6↦5),(8↦8↦8↦7),(8↦8↦9↦7),(8↦8↦9↦8),(9↦7↦1↦1),(9↦7↦1↦2),(9↦7↦1↦3),(9↦7↦2↦1),(9↦7↦2↦2),(9↦7↦2↦3),(9↦7↦3↦1),(9↦7↦3↦2),(9↦7↦3↦3),(9↦7↦4↦4),(9↦7↦4↦5),(9↦7↦4↦6),(9↦7↦5↦4),(9↦7↦5↦5),(9↦7↦5↦6),(9↦7↦6↦4),(9↦7↦6↦5),(9↦7↦6↦6),(9↦7↦7↦7),(9↦7↦7↦8),(9↦7↦7↦9),(9↦7↦8↦7),(9↦7↦8↦8),(9↦7↦8↦9),(9↦7↦9↦7),(9↦7↦9↦8),(9↦7↦9↦9),(9↦8↦1↦1),(9↦8↦1↦2),(9↦8↦1↦3),(9↦8↦2↦1),(9↦8↦2↦2),(9↦8↦2↦3),(9↦8↦3↦1),(9↦8↦3↦2),(9↦8↦3↦3),(9↦8↦4↦4),(9↦8↦4↦5),(9↦8↦4↦6),(9↦8↦5↦4),(9↦8↦5↦5),(9↦8↦5↦6),(9↦8↦6↦4),(9↦8↦6↦5),(9↦8↦6↦6),(9↦8↦7↦7),(9↦8↦7↦8),(9↦8↦7↦9),(9↦8↦8↦7),(9↦8↦8↦8),(9↦8↦8↦9),(9↦8↦9↦7),(9↦8↦9↦8),(9↦8↦9↦9),(9↦9↦2↦1),(9↦9↦3↦1),(9↦9↦3↦2),(9↦9↦5↦4),(9↦9↦6↦4),(9↦9↦6↦5),(9↦9↦8↦7),(9↦9↦9↦7),(9↦9↦9↦8)}
%% Cell type:markdown id: tags:
A full Sudoku solution, with distinct values in each row, column and sub-square, can now be found as follows:
%% Cell type:code id: tags:
``` prob
Board : DOM --> (DOM --> DOM) & !(x1,x2,y1,y2).((x1,x2,y1,y2):Diff => Board(x1)(y1) /= Board(x2)(y2))
```
%% Output
$\renewcommand{\emptyset}{\mathord\varnothing}\mathit{TRUE}$
**Solution:**
* $\mathit{Diff3} = \{(1\mapsto 1\mapsto 2\mapsto 1),(1\mapsto 1\mapsto 3\mapsto 1),(1\mapsto 1\mapsto 3\mapsto 2),(1\mapsto 1\mapsto 5\mapsto 4),(1\mapsto 1\mapsto 6\mapsto 4),(1\mapsto 1\mapsto 6\mapsto 5),(1\mapsto 1\mapsto 8\mapsto 7),(1\mapsto 1\mapsto 9\mapsto 7),(1\mapsto 1\mapsto 9\mapsto 8),(2\mapsto 1\mapsto 1\mapsto 1),(2\mapsto 1\mapsto 1\mapsto 2),(2\mapsto 1\mapsto 1\mapsto 3),(2\mapsto 1\mapsto 2\mapsto 1),(2\mapsto 1\mapsto 2\mapsto 2),(2\mapsto 1\mapsto 2\mapsto 3),(2\mapsto 1\mapsto 3\mapsto 1),(2\mapsto 1\mapsto 3\mapsto 2),(2\mapsto 1\mapsto 3\mapsto 3),(2\mapsto 1\mapsto 4\mapsto 4),(2\mapsto 1\mapsto 4\mapsto 5),(2\mapsto 1\mapsto 4\mapsto 6),(2\mapsto 1\mapsto 5\mapsto 4),(2\mapsto 1\mapsto 5\mapsto 5),(2\mapsto 1\mapsto 5\mapsto 6),(2\mapsto 1\mapsto 6\mapsto 4),(2\mapsto 1\mapsto 6\mapsto 5),(2\mapsto 1\mapsto 6\mapsto 6),(2\mapsto 1\mapsto 7\mapsto 7),(2\mapsto 1\mapsto 7\mapsto 8),(2\mapsto 1\mapsto 7\mapsto 9),(2\mapsto 1\mapsto 8\mapsto 7),(2\mapsto 1\mapsto 8\mapsto 8),(2\mapsto 1\mapsto 8\mapsto 9),(2\mapsto 1\mapsto 9\mapsto 7),(2\mapsto 1\mapsto 9\mapsto 8),(2\mapsto 1\mapsto 9\mapsto 9),(2\mapsto 2\mapsto 2\mapsto 1),(2\mapsto 2\mapsto 3\mapsto 1),(2\mapsto 2\mapsto 3\mapsto 2),(2\mapsto 2\mapsto 5\mapsto 4),(2\mapsto 2\mapsto 6\mapsto 4),(2\mapsto 2\mapsto 6\mapsto 5),(2\mapsto 2\mapsto 8\mapsto 7),(2\mapsto 2\mapsto 9\mapsto 7),(2\mapsto 2\mapsto 9\mapsto 8),(3\mapsto 1\mapsto 1\mapsto 1),(3\mapsto 1\mapsto 1\mapsto 2),(3\mapsto 1\mapsto 1\mapsto 3),(3\mapsto 1\mapsto 2\mapsto 1),(3\mapsto 1\mapsto 2\mapsto 2),(3\mapsto 1\mapsto 2\mapsto 3),(3\mapsto 1\mapsto 3\mapsto 1),(3\mapsto 1\mapsto 3\mapsto 2),(3\mapsto 1\mapsto 3\mapsto 3),(3\mapsto 1\mapsto 4\mapsto 4),(3\mapsto 1\mapsto 4\mapsto 5),(3\mapsto 1\mapsto 4\mapsto 6),(3\mapsto 1\mapsto 5\mapsto 4),(3\mapsto 1\mapsto 5\mapsto 5),(3\mapsto 1\mapsto 5\mapsto 6),(3\mapsto 1\mapsto 6\mapsto 4),(3\mapsto 1\mapsto 6\mapsto 5),(3\mapsto 1\mapsto 6\mapsto 6),(3\mapsto 1\mapsto 7\mapsto 7),(3\mapsto 1\mapsto 7\mapsto 8),(3\mapsto 1\mapsto 7\mapsto 9),(3\mapsto 1\mapsto 8\mapsto 7),(3\mapsto 1\mapsto 8\mapsto 8),(3\mapsto 1\mapsto 8\mapsto 9),(3\mapsto 1\mapsto 9\mapsto 7),(3\mapsto 1\mapsto 9\mapsto 8),(3\mapsto 1\mapsto 9\mapsto 9),(3\mapsto 2\mapsto 1\mapsto 1),(3\mapsto 2\mapsto 1\mapsto 2),(3\mapsto 2\mapsto 1\mapsto 3),(3\mapsto 2\mapsto 2\mapsto 1),(3\mapsto 2\mapsto 2\mapsto 2),(3\mapsto 2\mapsto 2\mapsto 3),(3\mapsto 2\mapsto 3\mapsto 1),(3\mapsto 2\mapsto 3\mapsto 2),(3\mapsto 2\mapsto 3\mapsto 3),(3\mapsto 2\mapsto 4\mapsto 4),(3\mapsto 2\mapsto 4\mapsto 5),(3\mapsto 2\mapsto 4\mapsto 6),(3\mapsto 2\mapsto 5\mapsto 4),(3\mapsto 2\mapsto 5\mapsto 5),(3\mapsto 2\mapsto 5\mapsto 6),(3\mapsto 2\mapsto 6\mapsto 4),(3\mapsto 2\mapsto 6\mapsto 5),(3\mapsto 2\mapsto 6\mapsto 6),(3\mapsto 2\mapsto 7\mapsto 7),(3\mapsto 2\mapsto 7\mapsto 8),(3\mapsto 2\mapsto 7\mapsto 9),(3\mapsto 2\mapsto 8\mapsto 7),(3\mapsto 2\mapsto 8\mapsto 8),(3\mapsto 2\mapsto 8\mapsto 9),(3\mapsto 2\mapsto 9\mapsto 7),(3\mapsto 2\mapsto 9\mapsto 8),(3\mapsto 2\mapsto 9\mapsto 9),(3\mapsto 3\mapsto 2\mapsto 1),(3\mapsto 3\mapsto 3\mapsto 1),(3\mapsto 3\mapsto 3\mapsto 2),(3\mapsto 3\mapsto 5\mapsto 4),(3\mapsto 3\mapsto 6\mapsto 4),(3\mapsto 3\mapsto 6\mapsto 5),(3\mapsto 3\mapsto 8\mapsto 7),(3\mapsto 3\mapsto 9\mapsto 7),(3\mapsto 3\mapsto 9\mapsto 8),(4\mapsto 4\mapsto 2\mapsto 1),(4\mapsto 4\mapsto 3\mapsto 1),(4\mapsto 4\mapsto 3\mapsto 2),(4\mapsto 4\mapsto 5\mapsto 4),(4\mapsto 4\mapsto 6\mapsto 4),(4\mapsto 4\mapsto 6\mapsto 5),(4\mapsto 4\mapsto 8\mapsto 7),(4\mapsto 4\mapsto 9\mapsto 7),(4\mapsto 4\mapsto 9\mapsto 8),(5\mapsto 4\mapsto 1\mapsto 1),(5\mapsto 4\mapsto 1\mapsto 2),(5\mapsto 4\mapsto 1\mapsto 3),(5\mapsto 4\mapsto 2\mapsto 1),(5\mapsto 4\mapsto 2\mapsto 2),(5\mapsto 4\mapsto 2\mapsto 3),(5\mapsto 4\mapsto 3\mapsto 1),(5\mapsto 4\mapsto 3\mapsto 2),(5\mapsto 4\mapsto 3\mapsto 3),(5\mapsto 4\mapsto 4\mapsto 4),(5\mapsto 4\mapsto 4\mapsto 5),(5\mapsto 4\mapsto 4\mapsto 6),(5\mapsto 4\mapsto 5\mapsto 4),(5\mapsto 4\mapsto 5\mapsto 5),(5\mapsto 4\mapsto 5\mapsto 6),(5\mapsto 4\mapsto 6\mapsto 4),(5\mapsto 4\mapsto 6\mapsto 5),(5\mapsto 4\mapsto 6\mapsto 6),(5\mapsto 4\mapsto 7\mapsto 7),(5\mapsto 4\mapsto 7\mapsto 8),(5\mapsto 4\mapsto 7\mapsto 9),(5\mapsto 4\mapsto 8\mapsto 7),(5\mapsto 4\mapsto 8\mapsto 8),(5\mapsto 4\mapsto 8\mapsto 9),(5\mapsto 4\mapsto 9\mapsto 7),(5\mapsto 4\mapsto 9\mapsto 8),(5\mapsto 4\mapsto 9\mapsto 9),(5\mapsto 5\mapsto 2\mapsto 1),(5\mapsto 5\mapsto 3\mapsto 1),(5\mapsto 5\mapsto 3\mapsto 2),(5\mapsto 5\mapsto 5\mapsto 4),(5\mapsto 5\mapsto 6\mapsto 4),(5\mapsto 5\mapsto 6\mapsto 5),(5\mapsto 5\mapsto 8\mapsto 7),(5\mapsto 5\mapsto 9\mapsto 7),(5\mapsto 5\mapsto 9\mapsto 8),(6\mapsto 4\mapsto 1\mapsto 1),(6\mapsto 4\mapsto 1\mapsto 2),(6\mapsto 4\mapsto 1\mapsto 3),(6\mapsto 4\mapsto 2\mapsto 1),(6\mapsto 4\mapsto 2\mapsto 2),(6\mapsto 4\mapsto 2\mapsto 3),(6\mapsto 4\mapsto 3\mapsto 1),(6\mapsto 4\mapsto 3\mapsto 2),(6\mapsto 4\mapsto 3\mapsto 3),(6\mapsto 4\mapsto 4\mapsto 4),(6\mapsto 4\mapsto 4\mapsto 5),(6\mapsto 4\mapsto 4\mapsto 6),(6\mapsto 4\mapsto 5\mapsto 4),(6\mapsto 4\mapsto 5\mapsto 5),(6\mapsto 4\mapsto 5\mapsto 6),(6\mapsto 4\mapsto 6\mapsto 4),(6\mapsto 4\mapsto 6\mapsto 5),(6\mapsto 4\mapsto 6\mapsto 6),(6\mapsto 4\mapsto 7\mapsto 7),(6\mapsto 4\mapsto 7\mapsto 8),(6\mapsto 4\mapsto 7\mapsto 9),(6\mapsto 4\mapsto 8\mapsto 7),(6\mapsto 4\mapsto 8\mapsto 8),(6\mapsto 4\mapsto 8\mapsto 9),(6\mapsto 4\mapsto 9\mapsto 7),(6\mapsto 4\mapsto 9\mapsto 8),(6\mapsto 4\mapsto 9\mapsto 9),(6\mapsto 5\mapsto 1\mapsto 1),(6\mapsto 5\mapsto 1\mapsto 2),(6\mapsto 5\mapsto 1\mapsto 3),(6\mapsto 5\mapsto 2\mapsto 1),(6\mapsto 5\mapsto 2\mapsto 2),(6\mapsto 5\mapsto 2\mapsto 3),(6\mapsto 5\mapsto 3\mapsto 1),(6\mapsto 5\mapsto 3\mapsto 2),(6\mapsto 5\mapsto 3\mapsto 3),(6\mapsto 5\mapsto 4\mapsto 4),(6\mapsto 5\mapsto 4\mapsto 5),(6\mapsto 5\mapsto 4\mapsto 6),(6\mapsto 5\mapsto 5\mapsto 4),(6\mapsto 5\mapsto 5\mapsto 5),(6\mapsto 5\mapsto 5\mapsto 6),(6\mapsto 5\mapsto 6\mapsto 4),(6\mapsto 5\mapsto 6\mapsto 5),(6\mapsto 5\mapsto 6\mapsto 6),(6\mapsto 5\mapsto 7\mapsto 7),(6\mapsto 5\mapsto 7\mapsto 8),(6\mapsto 5\mapsto 7\mapsto 9),(6\mapsto 5\mapsto 8\mapsto 7),(6\mapsto 5\mapsto 8\mapsto 8),(6\mapsto 5\mapsto 8\mapsto 9),(6\mapsto 5\mapsto 9\mapsto 7),(6\mapsto 5\mapsto 9\mapsto 8),(6\mapsto 5\mapsto 9\mapsto 9),(6\mapsto 6\mapsto 2\mapsto 1),(6\mapsto 6\mapsto 3\mapsto 1),(6\mapsto 6\mapsto 3\mapsto 2),(6\mapsto 6\mapsto 5\mapsto 4),(6\mapsto 6\mapsto 6\mapsto 4),(6\mapsto 6\mapsto 6\mapsto 5),(6\mapsto 6\mapsto 8\mapsto 7),(6\mapsto 6\mapsto 9\mapsto 7),(6\mapsto 6\mapsto 9\mapsto 8),(7\mapsto 7\mapsto 2\mapsto 1),(7\mapsto 7\mapsto 3\mapsto 1),(7\mapsto 7\mapsto 3\mapsto 2),(7\mapsto 7\mapsto 5\mapsto 4),(7\mapsto 7\mapsto 6\mapsto 4),(7\mapsto 7\mapsto 6\mapsto 5),(7\mapsto 7\mapsto 8\mapsto 7),(7\mapsto 7\mapsto 9\mapsto 7),(7\mapsto 7\mapsto 9\mapsto 8),(8\mapsto 7\mapsto 1\mapsto 1),(8\mapsto 7\mapsto 1\mapsto 2),(8\mapsto 7\mapsto 1\mapsto 3),(8\mapsto 7\mapsto 2\mapsto 1),(8\mapsto 7\mapsto 2\mapsto 2),(8\mapsto 7\mapsto 2\mapsto 3),(8\mapsto 7\mapsto 3\mapsto 1),(8\mapsto 7\mapsto 3\mapsto 2),(8\mapsto 7\mapsto 3\mapsto 3),(8\mapsto 7\mapsto 4\mapsto 4),(8\mapsto 7\mapsto 4\mapsto 5),(8\mapsto 7\mapsto 4\mapsto 6),(8\mapsto 7\mapsto 5\mapsto 4),(8\mapsto 7\mapsto 5\mapsto 5),(8\mapsto 7\mapsto 5\mapsto 6),(8\mapsto 7\mapsto 6\mapsto 4),(8\mapsto 7\mapsto 6\mapsto 5),(8\mapsto 7\mapsto 6\mapsto 6),(8\mapsto 7\mapsto 7\mapsto 7),(8\mapsto 7\mapsto 7\mapsto 8),(8\mapsto 7\mapsto 7\mapsto 9),(8\mapsto 7\mapsto 8\mapsto 7),(8\mapsto 7\mapsto 8\mapsto 8),(8\mapsto 7\mapsto 8\mapsto 9),(8\mapsto 7\mapsto 9\mapsto 7),(8\mapsto 7\mapsto 9\mapsto 8),(8\mapsto 7\mapsto 9\mapsto 9),(8\mapsto 8\mapsto 2\mapsto 1),(8\mapsto 8\mapsto 3\mapsto 1),(8\mapsto 8\mapsto 3\mapsto 2),(8\mapsto 8\mapsto 5\mapsto 4),(8\mapsto 8\mapsto 6\mapsto 4),(8\mapsto 8\mapsto 6\mapsto 5),(8\mapsto 8\mapsto 8\mapsto 7),(8\mapsto 8\mapsto 9\mapsto 7),(8\mapsto 8\mapsto 9\mapsto 8),(9\mapsto 7\mapsto 1\mapsto 1),(9\mapsto 7\mapsto 1\mapsto 2),(9\mapsto 7\mapsto 1\mapsto 3),(9\mapsto 7\mapsto 2\mapsto 1),(9\mapsto 7\mapsto 2\mapsto 2),(9\mapsto 7\mapsto 2\mapsto 3),(9\mapsto 7\mapsto 3\mapsto 1),(9\mapsto 7\mapsto 3\mapsto 2),(9\mapsto 7\mapsto 3\mapsto 3),(9\mapsto 7\mapsto 4\mapsto 4),(9\mapsto 7\mapsto 4\mapsto 5),(9\mapsto 7\mapsto 4\mapsto 6),(9\mapsto 7\mapsto 5\mapsto 4),(9\mapsto 7\mapsto 5\mapsto 5),(9\mapsto 7\mapsto 5\mapsto 6),(9\mapsto 7\mapsto 6\mapsto 4),(9\mapsto 7\mapsto 6\mapsto 5),(9\mapsto 7\mapsto 6\mapsto 6),(9\mapsto 7\mapsto 7\mapsto 7),(9\mapsto 7\mapsto 7\mapsto 8),(9\mapsto 7\mapsto 7\mapsto 9),(9\mapsto 7\mapsto 8\mapsto 7),(9\mapsto 7\mapsto 8\mapsto 8),(9\mapsto 7\mapsto 8\mapsto 9),(9\mapsto 7\mapsto 9\mapsto 7),(9\mapsto 7\mapsto 9\mapsto 8),(9\mapsto 7\mapsto 9\mapsto 9),(9\mapsto 8\mapsto 1\mapsto 1),(9\mapsto 8\mapsto 1\mapsto 2),(9\mapsto 8\mapsto 1\mapsto 3),(9\mapsto 8\mapsto 2\mapsto 1),(9\mapsto 8\mapsto 2\mapsto 2),(9\mapsto 8\mapsto 2\mapsto 3),(9\mapsto 8\mapsto 3\mapsto 1),(9\mapsto 8\mapsto 3\mapsto 2),(9\mapsto 8\mapsto 3\mapsto 3),(9\mapsto 8\mapsto 4\mapsto 4),(9\mapsto 8\mapsto 4\mapsto 5),(9\mapsto 8\mapsto 4\mapsto 6),(9\mapsto 8\mapsto 5\mapsto 4),(9\mapsto 8\mapsto 5\mapsto 5),(9\mapsto 8\mapsto 5\mapsto 6),(9\mapsto 8\mapsto 6\mapsto 4),(9\mapsto 8\mapsto 6\mapsto 5),(9\mapsto 8\mapsto 6\mapsto 6),(9\mapsto 8\mapsto 7\mapsto 7),(9\mapsto 8\mapsto 7\mapsto 8),(9\mapsto 8\mapsto 7\mapsto 9),(9\mapsto 8\mapsto 8\mapsto 7),(9\mapsto 8\mapsto 8\mapsto 8),(9\mapsto 8\mapsto 8\mapsto 9),(9\mapsto 8\mapsto 9\mapsto 7),(9\mapsto 8\mapsto 9\mapsto 8),(9\mapsto 8\mapsto 9\mapsto 9),(9\mapsto 9\mapsto 2\mapsto 1),(9\mapsto 9\mapsto 3\mapsto 1),(9\mapsto 9\mapsto 3\mapsto 2),(9\mapsto 9\mapsto 5\mapsto 4),(9\mapsto 9\mapsto 6\mapsto 4),(9\mapsto 9\mapsto 6\mapsto 5),(9\mapsto 9\mapsto 8\mapsto 7),(9\mapsto 9\mapsto 9\mapsto 7),(9\mapsto 9\mapsto 9\mapsto 8)\}$
* $\mathit{Diff2} = \{(1\mapsto 1\mapsto 1\mapsto 2),(1\mapsto 1\mapsto 1\mapsto 3),(1\mapsto 1\mapsto 1\mapsto 4),(1\mapsto 1\mapsto 1\mapsto 5),(1\mapsto 1\mapsto 1\mapsto 6),(1\mapsto 1\mapsto 1\mapsto 7),(1\mapsto 1\mapsto 1\mapsto 8),(1\mapsto 1\mapsto 1\mapsto 9),(1\mapsto 1\mapsto 2\mapsto 3),(1\mapsto 1\mapsto 2\mapsto 4),(1\mapsto 1\mapsto 2\mapsto 5),(1\mapsto 1\mapsto 2\mapsto 6),(1\mapsto 1\mapsto 2\mapsto 7),(1\mapsto 1\mapsto 2\mapsto 8),(1\mapsto 1\mapsto 2\mapsto 9),(1\mapsto 1\mapsto 3\mapsto 4),(1\mapsto 1\mapsto 3\mapsto 5),(1\mapsto 1\mapsto 3\mapsto 6),(1\mapsto 1\mapsto 3\mapsto 7),(1\mapsto 1\mapsto 3\mapsto 8),(1\mapsto 1\mapsto 3\mapsto 9),(1\mapsto 1\mapsto 4\mapsto 5),(1\mapsto 1\mapsto 4\mapsto 6),(1\mapsto 1\mapsto 4\mapsto 7),(1\mapsto 1\mapsto 4\mapsto 8),(1\mapsto 1\mapsto 4\mapsto 9),(1\mapsto 1\mapsto 5\mapsto 6),(1\mapsto 1\mapsto 5\mapsto 7),(1\mapsto 1\mapsto 5\mapsto 8),(1\mapsto 1\mapsto 5\mapsto 9),(1\mapsto 1\mapsto 6\mapsto 7),(1\mapsto 1\mapsto 6\mapsto 8),(1\mapsto 1\mapsto 6\mapsto 9),(1\mapsto 1\mapsto 7\mapsto 8),(1\mapsto 1\mapsto 7\mapsto 9),(1\mapsto 1\mapsto 8\mapsto 9),(2\mapsto 2\mapsto 1\mapsto 2),(2\mapsto 2\mapsto 1\mapsto 3),(2\mapsto 2\mapsto 1\mapsto 4),(2\mapsto 2\mapsto 1\mapsto 5),(2\mapsto 2\mapsto 1\mapsto 6),(2\mapsto 2\mapsto 1\mapsto 7),(2\mapsto 2\mapsto 1\mapsto 8),(2\mapsto 2\mapsto 1\mapsto 9),(2\mapsto 2\mapsto 2\mapsto 3),(2\mapsto 2\mapsto 2\mapsto 4),(2\mapsto 2\mapsto 2\mapsto 5),(2\mapsto 2\mapsto 2\mapsto 6),(2\mapsto 2\mapsto 2\mapsto 7),(2\mapsto 2\mapsto 2\mapsto 8),(2\mapsto 2\mapsto 2\mapsto 9),(2\mapsto 2\mapsto 3\mapsto 4),(2\mapsto 2\mapsto 3\mapsto 5),(2\mapsto 2\mapsto 3\mapsto 6),(2\mapsto 2\mapsto 3\mapsto 7),(2\mapsto 2\mapsto 3\mapsto 8),(2\mapsto 2\mapsto 3\mapsto 9),(2\mapsto 2\mapsto 4\mapsto 5),(2\mapsto 2\mapsto 4\mapsto 6),(2\mapsto 2\mapsto 4\mapsto 7),(2\mapsto 2\mapsto 4\mapsto 8),(2\mapsto 2\mapsto 4\mapsto 9),(2\mapsto 2\mapsto 5\mapsto 6),(2\mapsto 2\mapsto 5\mapsto 7),(2\mapsto 2\mapsto 5\mapsto 8),(2\mapsto 2\mapsto 5\mapsto 9),(2\mapsto 2\mapsto 6\mapsto 7),(2\mapsto 2\mapsto 6\mapsto 8),(2\mapsto 2\mapsto 6\mapsto 9),(2\mapsto 2\mapsto 7\mapsto 8),(2\mapsto 2\mapsto 7\mapsto 9),(2\mapsto 2\mapsto 8\mapsto 9),(3\mapsto 3\mapsto 1\mapsto 2),(3\mapsto 3\mapsto 1\mapsto 3),(3\mapsto 3\mapsto 1\mapsto 4),(3\mapsto 3\mapsto 1\mapsto 5),(3\mapsto 3\mapsto 1\mapsto 6),(3\mapsto 3\mapsto 1\mapsto 7),(3\mapsto 3\mapsto 1\mapsto 8),(3\mapsto 3\mapsto 1\mapsto 9),(3\mapsto 3\mapsto 2\mapsto 3),(3\mapsto 3\mapsto 2\mapsto 4),(3\mapsto 3\mapsto 2\mapsto 5),(3\mapsto 3\mapsto 2\mapsto 6),(3\mapsto 3\mapsto 2\mapsto 7),(3\mapsto 3\mapsto 2\mapsto 8),(3\mapsto 3\mapsto 2\mapsto 9),(3\mapsto 3\mapsto 3\mapsto 4),(3\mapsto 3\mapsto 3\mapsto 5),(3\mapsto 3\mapsto 3\mapsto 6),(3\mapsto 3\mapsto 3\mapsto 7),(3\mapsto 3\mapsto 3\mapsto 8),(3\mapsto 3\mapsto 3\mapsto 9),(3\mapsto 3\mapsto 4\mapsto 5),(3\mapsto 3\mapsto 4\mapsto 6),(3\mapsto 3\mapsto 4\mapsto 7),(3\mapsto 3\mapsto 4\mapsto 8),(3\mapsto 3\mapsto 4\mapsto 9),(3\mapsto 3\mapsto 5\mapsto 6),(3\mapsto 3\mapsto 5\mapsto 7),(3\mapsto 3\mapsto 5\mapsto 8),(3\mapsto 3\mapsto 5\mapsto 9),(3\mapsto 3\mapsto 6\mapsto 7),(3\mapsto 3\mapsto 6\mapsto 8),(3\mapsto 3\mapsto 6\mapsto 9),(3\mapsto 3\mapsto 7\mapsto 8),(3\mapsto 3\mapsto 7\mapsto 9),(3\mapsto 3\mapsto 8\mapsto 9),(4\mapsto 4\mapsto 1\mapsto 2),(4\mapsto 4\mapsto 1\mapsto 3),(4\mapsto 4\mapsto 1\mapsto 4),(4\mapsto 4\mapsto 1\mapsto 5),(4\mapsto 4\mapsto 1\mapsto 6),(4\mapsto 4\mapsto 1\mapsto 7),(4\mapsto 4\mapsto 1\mapsto 8),(4\mapsto 4\mapsto 1\mapsto 9),(4\mapsto 4\mapsto 2\mapsto 3),(4\mapsto 4\mapsto 2\mapsto 4),(4\mapsto 4\mapsto 2\mapsto 5),(4\mapsto 4\mapsto 2\mapsto 6),(4\mapsto 4\mapsto 2\mapsto 7),(4\mapsto 4\mapsto 2\mapsto 8),(4\mapsto 4\mapsto 2\mapsto 9),(4\mapsto 4\mapsto 3\mapsto 4),(4\mapsto 4\mapsto 3\mapsto 5),(4\mapsto 4\mapsto 3\mapsto 6),(4\mapsto 4\mapsto 3\mapsto 7),(4\mapsto 4\mapsto 3\mapsto 8),(4\mapsto 4\mapsto 3\mapsto 9),(4\mapsto 4\mapsto 4\mapsto 5),(4\mapsto 4\mapsto 4\mapsto 6),(4\mapsto 4\mapsto 4\mapsto 7),(4\mapsto 4\mapsto 4\mapsto 8),(4\mapsto 4\mapsto 4\mapsto 9),(4\mapsto 4\mapsto 5\mapsto 6),(4\mapsto 4\mapsto 5\mapsto 7),(4\mapsto 4\mapsto 5\mapsto 8),(4\mapsto 4\mapsto 5\mapsto 9),(4\mapsto 4\mapsto 6\mapsto 7),(4\mapsto 4\mapsto 6\mapsto 8),(4\mapsto 4\mapsto 6\mapsto 9),(4\mapsto 4\mapsto 7\mapsto 8),(4\mapsto 4\mapsto 7\mapsto 9),(4\mapsto 4\mapsto 8\mapsto 9),(5\mapsto 5\mapsto 1\mapsto 2),(5\mapsto 5\mapsto 1\mapsto 3),(5\mapsto 5\mapsto 1\mapsto 4),(5\mapsto 5\mapsto 1\mapsto 5),(5\mapsto 5\mapsto 1\mapsto 6),(5\mapsto 5\mapsto 1\mapsto 7),(5\mapsto 5\mapsto 1\mapsto 8),(5\mapsto 5\mapsto 1\mapsto 9),(5\mapsto 5\mapsto 2\mapsto 3),(5\mapsto 5\mapsto 2\mapsto 4),(5\mapsto 5\mapsto 2\mapsto 5),(5\mapsto 5\mapsto 2\mapsto 6),(5\mapsto 5\mapsto 2\mapsto 7),(5\mapsto 5\mapsto 2\mapsto 8),(5\mapsto 5\mapsto 2\mapsto 9),(5\mapsto 5\mapsto 3\mapsto 4),(5\mapsto 5\mapsto 3\mapsto 5),(5\mapsto 5\mapsto 3\mapsto 6),(5\mapsto 5\mapsto 3\mapsto 7),(5\mapsto 5\mapsto 3\mapsto 8),(5\mapsto 5\mapsto 3\mapsto 9),(5\mapsto 5\mapsto 4\mapsto 5),(5\mapsto 5\mapsto 4\mapsto 6),(5\mapsto 5\mapsto 4\mapsto 7),(5\mapsto 5\mapsto 4\mapsto 8),(5\mapsto 5\mapsto 4\mapsto 9),(5\mapsto 5\mapsto 5\mapsto 6),(5\mapsto 5\mapsto 5\mapsto 7),(5\mapsto 5\mapsto 5\mapsto 8),(5\mapsto 5\mapsto 5\mapsto 9),(5\mapsto 5\mapsto 6\mapsto 7),(5\mapsto 5\mapsto 6\mapsto 8),(5\mapsto 5\mapsto 6\mapsto 9),(5\mapsto 5\mapsto 7\mapsto 8),(5\mapsto 5\mapsto 7\mapsto 9),(5\mapsto 5\mapsto 8\mapsto 9),(6\mapsto 6\mapsto 1\mapsto 2),(6\mapsto 6\mapsto 1\mapsto 3),(6\mapsto 6\mapsto 1\mapsto 4),(6\mapsto 6\mapsto 1\mapsto 5),(6\mapsto 6\mapsto 1\mapsto 6),(6\mapsto 6\mapsto 1\mapsto 7),(6\mapsto 6\mapsto 1\mapsto 8),(6\mapsto 6\mapsto 1\mapsto 9),(6\mapsto 6\mapsto 2\mapsto 3),(6\mapsto 6\mapsto 2\mapsto 4),(6\mapsto 6\mapsto 2\mapsto 5),(6\mapsto 6\mapsto 2\mapsto 6),(6\mapsto 6\mapsto 2\mapsto 7),(6\mapsto 6\mapsto 2\mapsto 8),(6\mapsto 6\mapsto 2\mapsto 9),(6\mapsto 6\mapsto 3\mapsto 4),(6\mapsto 6\mapsto 3\mapsto 5),(6\mapsto 6\mapsto 3\mapsto 6),(6\mapsto 6\mapsto 3\mapsto 7),(6\mapsto 6\mapsto 3\mapsto 8),(6\mapsto 6\mapsto 3\mapsto 9),(6\mapsto 6\mapsto 4\mapsto 5),(6\mapsto 6\mapsto 4\mapsto 6),(6\mapsto 6\mapsto 4\mapsto 7),(6\mapsto 6\mapsto 4\mapsto 8),(6\mapsto 6\mapsto 4\mapsto 9),(6\mapsto 6\mapsto 5\mapsto 6),(6\mapsto 6\mapsto 5\mapsto 7),(6\mapsto 6\mapsto 5\mapsto 8),(6\mapsto 6\mapsto 5\mapsto 9),(6\mapsto 6\mapsto 6\mapsto 7),(6\mapsto 6\mapsto 6\mapsto 8),(6\mapsto 6\mapsto 6\mapsto 9),(6\mapsto 6\mapsto 7\mapsto 8),(6\mapsto 6\mapsto 7\mapsto 9),(6\mapsto 6\mapsto 8\mapsto 9),(7\mapsto 7\mapsto 1\mapsto 2),(7\mapsto 7\mapsto 1\mapsto 3),(7\mapsto 7\mapsto 1\mapsto 4),(7\mapsto 7\mapsto 1\mapsto 5),(7\mapsto 7\mapsto 1\mapsto 6),(7\mapsto 7\mapsto 1\mapsto 7),(7\mapsto 7\mapsto 1\mapsto 8),(7\mapsto 7\mapsto 1\mapsto 9),(7\mapsto 7\mapsto 2\mapsto 3),(7\mapsto 7\mapsto 2\mapsto 4),(7\mapsto 7\mapsto 2\mapsto 5),(7\mapsto 7\mapsto 2\mapsto 6),(7\mapsto 7\mapsto 2\mapsto 7),(7\mapsto 7\mapsto 2\mapsto 8),(7\mapsto 7\mapsto 2\mapsto 9),(7\mapsto 7\mapsto 3\mapsto 4),(7\mapsto 7\mapsto 3\mapsto 5),(7\mapsto 7\mapsto 3\mapsto 6),(7\mapsto 7\mapsto 3\mapsto 7),(7\mapsto 7\mapsto 3\mapsto 8),(7\mapsto 7\mapsto 3\mapsto 9),(7\mapsto 7\mapsto 4\mapsto 5),(7\mapsto 7\mapsto 4\mapsto 6),(7\mapsto 7\mapsto 4\mapsto 7),(7\mapsto 7\mapsto 4\mapsto 8),(7\mapsto 7\mapsto 4\mapsto 9),(7\mapsto 7\mapsto 5\mapsto 6),(7\mapsto 7\mapsto 5\mapsto 7),(7\mapsto 7\mapsto 5\mapsto 8),(7\mapsto 7\mapsto 5\mapsto 9),(7\mapsto 7\mapsto 6\mapsto 7),(7\mapsto 7\mapsto 6\mapsto 8),(7\mapsto 7\mapsto 6\mapsto 9),(7\mapsto 7\mapsto 7\mapsto 8),(7\mapsto 7\mapsto 7\mapsto 9),(7\mapsto 7\mapsto 8\mapsto 9),(8\mapsto 8\mapsto 1\mapsto 2),(8\mapsto 8\mapsto 1\mapsto 3),(8\mapsto 8\mapsto 1\mapsto 4),(8\mapsto 8\mapsto 1\mapsto 5),(8\mapsto 8\mapsto 1\mapsto 6),(8\mapsto 8\mapsto 1\mapsto 7),(8\mapsto 8\mapsto 1\mapsto 8),(8\mapsto 8\mapsto 1\mapsto 9),(8\mapsto 8\mapsto 2\mapsto 3),(8\mapsto 8\mapsto 2\mapsto 4),(8\mapsto 8\mapsto 2\mapsto 5),(8\mapsto 8\mapsto 2\mapsto 6),(8\mapsto 8\mapsto 2\mapsto 7),(8\mapsto 8\mapsto 2\mapsto 8),(8\mapsto 8\mapsto 2\mapsto 9),(8\mapsto 8\mapsto 3\mapsto 4),(8\mapsto 8\mapsto 3\mapsto 5),(8\mapsto 8\mapsto 3\mapsto 6),(8\mapsto 8\mapsto 3\mapsto 7),(8\mapsto 8\mapsto 3\mapsto 8),(8\mapsto 8\mapsto 3\mapsto 9),(8\mapsto 8\mapsto 4\mapsto 5),(8\mapsto 8\mapsto 4\mapsto 6),(8\mapsto 8\mapsto 4\mapsto 7),(8\mapsto 8\mapsto 4\mapsto 8),(8\mapsto 8\mapsto 4\mapsto 9),(8\mapsto 8\mapsto 5\mapsto 6),(8\mapsto 8\mapsto 5\mapsto 7),(8\mapsto 8\mapsto 5\mapsto 8),(8\mapsto 8\mapsto 5\mapsto 9),(8\mapsto 8\mapsto 6\mapsto 7),(8\mapsto 8\mapsto 6\mapsto 8),(8\mapsto 8\mapsto 6\mapsto 9),(8\mapsto 8\mapsto 7\mapsto 8),(8\mapsto 8\mapsto 7\mapsto 9),(8\mapsto 8\mapsto 8\mapsto 9),(9\mapsto 9\mapsto 1\mapsto 2),(9\mapsto 9\mapsto 1\mapsto 3),(9\mapsto 9\mapsto 1\mapsto 4),(9\mapsto 9\mapsto 1\mapsto 5),(9\mapsto 9\mapsto 1\mapsto 6),(9\mapsto 9\mapsto 1\mapsto 7),(9\mapsto 9\mapsto 1\mapsto 8),(9\mapsto 9\mapsto 1\mapsto 9),(9\mapsto 9\mapsto 2\mapsto 3),(9\mapsto 9\mapsto 2\mapsto 4),(9\mapsto 9\mapsto 2\mapsto 5),(9\mapsto 9\mapsto 2\mapsto 6),(9\mapsto 9\mapsto 2\mapsto 7),(9\mapsto 9\mapsto 2\mapsto 8),(9\mapsto 9\mapsto 2\mapsto 9),(9\mapsto 9\mapsto 3\mapsto 4),(9\mapsto 9\mapsto 3\mapsto 5),(9\mapsto 9\mapsto 3\mapsto 6),(9\mapsto 9\mapsto 3\mapsto 7),(9\mapsto 9\mapsto 3\mapsto 8),(9\mapsto 9\mapsto 3\mapsto 9),(9\mapsto 9\mapsto 4\mapsto 5),(9\mapsto 9\mapsto 4\mapsto 6),(9\mapsto 9\mapsto 4\mapsto 7),(9\mapsto 9\mapsto 4\mapsto 8),(9\mapsto 9\mapsto 4\mapsto 9),(9\mapsto 9\mapsto 5\mapsto 6),(9\mapsto 9\mapsto 5\mapsto 7),(9\mapsto 9\mapsto 5\mapsto 8),(9\mapsto 9\mapsto 5\mapsto 9),(9\mapsto 9\mapsto 6\mapsto 7),(9\mapsto 9\mapsto 6\mapsto 8),(9\mapsto 9\mapsto 6\mapsto 9),(9\mapsto 9\mapsto 7\mapsto 8),(9\mapsto 9\mapsto 7\mapsto 9),(9\mapsto 9\mapsto 8\mapsto 9)\}$
* $\mathit{Board} = \{(1\mapsto\{(1\mapsto 1),(2\mapsto 1),(3\mapsto 1),(4\mapsto 1),(5\mapsto 1),(6\mapsto 1),(7\mapsto 1),(8\mapsto 1),(9\mapsto 1)\}),(2\mapsto\{(1\mapsto 1),(2\mapsto 1),(3\mapsto 1),(4\mapsto 1),(5\mapsto 1),(6\mapsto 1),(7\mapsto 1),(8\mapsto 1),(9\mapsto 1)\}),(3\mapsto\{(1\mapsto 1),(2\mapsto 1),(3\mapsto 1),(4\mapsto 1),(5\mapsto 1),(6\mapsto 1),(7\mapsto 1),(8\mapsto 1),(9\mapsto 1)\}),(4\mapsto\{(1\mapsto 1),(2\mapsto 1),(3\mapsto 1),(4\mapsto 1),(5\mapsto 1),(6\mapsto 1),(7\mapsto 1),(8\mapsto 1),(9\mapsto 1)\}),(5\mapsto\{(1\mapsto 1),(2\mapsto 1),(3\mapsto 1),(4\mapsto 1),(5\mapsto 1),(6\mapsto 1),(7\mapsto 1),(8\mapsto 1),(9\mapsto 1)\}),(6\mapsto\{(1\mapsto 1),(2\mapsto 1),(3\mapsto 1),(4\mapsto 1),(5\mapsto 1),(6\mapsto 1),(7\mapsto 1),(8\mapsto 1),(9\mapsto 1)\}),(7\mapsto\{(1\mapsto 1),(2\mapsto 1),(3\mapsto 1),(4\mapsto 1),(5\mapsto 1),(6\mapsto 1),(7\mapsto 1),(8\mapsto 1),(9\mapsto 1)\}),(8\mapsto\{(1\mapsto 1),(2\mapsto 1),(3\mapsto 1),(4\mapsto 1),(5\mapsto 1),(6\mapsto 1),(7\mapsto 1),(8\mapsto 1),(9\mapsto 1)\}),(9\mapsto\{(1\mapsto 1),(2\mapsto 1),(3\mapsto 1),(4\mapsto 1),(5\mapsto 1),(6\mapsto 1),(7\mapsto 1),(8\mapsto 1),(9\mapsto 1)\})\}$
* $\mathit{DOM} = \{1,2,3,4,5,6,7,8,9\}$
* $\mathit{Diff1} = \{(1\mapsto 2\mapsto 1\mapsto 1),(1\mapsto 2\mapsto 2\mapsto 2),(1\mapsto 2\mapsto 3\mapsto 3),(1\mapsto 2\mapsto 4\mapsto 4),(1\mapsto 2\mapsto 5\mapsto 5),(1\mapsto 2\mapsto 6\mapsto 6),(1\mapsto 2\mapsto 7\mapsto 7),(1\mapsto 2\mapsto 8\mapsto 8),(1\mapsto 2\mapsto 9\mapsto 9),(1\mapsto 3\mapsto 1\mapsto 1),(1\mapsto 3\mapsto 2\mapsto 2),(1\mapsto 3\mapsto 3\mapsto 3),(1\mapsto 3\mapsto 4\mapsto 4),(1\mapsto 3\mapsto 5\mapsto 5),(1\mapsto 3\mapsto 6\mapsto 6),(1\mapsto 3\mapsto 7\mapsto 7),(1\mapsto 3\mapsto 8\mapsto 8),(1\mapsto 3\mapsto 9\mapsto 9),(1\mapsto 4\mapsto 1\mapsto 1),(1\mapsto 4\mapsto 2\mapsto 2),(1\mapsto 4\mapsto 3\mapsto 3),(1\mapsto 4\mapsto 4\mapsto 4),(1\mapsto 4\mapsto 5\mapsto 5),(1\mapsto 4\mapsto 6\mapsto 6),(1\mapsto 4\mapsto 7\mapsto 7),(1\mapsto 4\mapsto 8\mapsto 8),(1\mapsto 4\mapsto 9\mapsto 9),(1\mapsto 5\mapsto 1\mapsto 1),(1\mapsto 5\mapsto 2\mapsto 2),(1\mapsto 5\mapsto 3\mapsto 3),(1\mapsto 5\mapsto 4\mapsto 4),(1\mapsto 5\mapsto 5\mapsto 5),(1\mapsto 5\mapsto 6\mapsto 6),(1\mapsto 5\mapsto 7\mapsto 7),(1\mapsto 5\mapsto 8\mapsto 8),(1\mapsto 5\mapsto 9\mapsto 9),(1\mapsto 6\mapsto 1\mapsto 1),(1\mapsto 6\mapsto 2\mapsto 2),(1\mapsto 6\mapsto 3\mapsto 3),(1\mapsto 6\mapsto 4\mapsto 4),(1\mapsto 6\mapsto 5\mapsto 5),(1\mapsto 6\mapsto 6\mapsto 6),(1\mapsto 6\mapsto 7\mapsto 7),(1\mapsto 6\mapsto 8\mapsto 8),(1\mapsto 6\mapsto 9\mapsto 9),(1\mapsto 7\mapsto 1\mapsto 1),(1\mapsto 7\mapsto 2\mapsto 2),(1\mapsto 7\mapsto 3\mapsto 3),(1\mapsto 7\mapsto 4\mapsto 4),(1\mapsto 7\mapsto 5\mapsto 5),(1\mapsto 7\mapsto 6\mapsto 6),(1\mapsto 7\mapsto 7\mapsto 7),(1\mapsto 7\mapsto 8\mapsto 8),(1\mapsto 7\mapsto 9\mapsto 9),(1\mapsto 8\mapsto 1\mapsto 1),(1\mapsto 8\mapsto 2\mapsto 2),(1\mapsto 8\mapsto 3\mapsto 3),(1\mapsto 8\mapsto 4\mapsto 4),(1\mapsto 8\mapsto 5\mapsto 5),(1\mapsto 8\mapsto 6\mapsto 6),(1\mapsto 8\mapsto 7\mapsto 7),(1\mapsto 8\mapsto 8\mapsto 8),(1\mapsto 8\mapsto 9\mapsto 9),(1\mapsto 9\mapsto 1\mapsto 1),(1\mapsto 9\mapsto 2\mapsto 2),(1\mapsto 9\mapsto 3\mapsto 3),(1\mapsto 9\mapsto 4\mapsto 4),(1\mapsto 9\mapsto 5\mapsto 5),(1\mapsto 9\mapsto 6\mapsto 6),(1\mapsto 9\mapsto 7\mapsto 7),(1\mapsto 9\mapsto 8\mapsto 8),(1\mapsto 9\mapsto 9\mapsto 9),(2\mapsto 3\mapsto 1\mapsto 1),(2\mapsto 3\mapsto 2\mapsto 2),(2\mapsto 3\mapsto 3\mapsto 3),(2\mapsto 3\mapsto 4\mapsto 4),(2\mapsto 3\mapsto 5\mapsto 5),(2\mapsto 3\mapsto 6\mapsto 6),(2\mapsto 3\mapsto 7\mapsto 7),(2\mapsto 3\mapsto 8\mapsto 8),(2\mapsto 3\mapsto 9\mapsto 9),(2\mapsto 4\mapsto 1\mapsto 1),(2\mapsto 4\mapsto 2\mapsto 2),(2\mapsto 4\mapsto 3\mapsto 3),(2\mapsto 4\mapsto 4\mapsto 4),(2\mapsto 4\mapsto 5\mapsto 5),(2\mapsto 4\mapsto 6\mapsto 6),(2\mapsto 4\mapsto 7\mapsto 7),(2\mapsto 4\mapsto 8\mapsto 8),(2\mapsto 4\mapsto 9\mapsto 9),(2\mapsto 5\mapsto 1\mapsto 1),(2\mapsto 5\mapsto 2\mapsto 2),(2\mapsto 5\mapsto 3\mapsto 3),(2\mapsto 5\mapsto 4\mapsto 4),(2\mapsto 5\mapsto 5\mapsto 5),(2\mapsto 5\mapsto 6\mapsto 6),(2\mapsto 5\mapsto 7\mapsto 7),(2\mapsto 5\mapsto 8\mapsto 8),(2\mapsto 5\mapsto 9\mapsto 9),(2\mapsto 6\mapsto 1\mapsto 1),(2\mapsto 6\mapsto 2\mapsto 2),(2\mapsto 6\mapsto 3\mapsto 3),(2\mapsto 6\mapsto 4\mapsto 4),(2\mapsto 6\mapsto 5\mapsto 5),(2\mapsto 6\mapsto 6\mapsto 6),(2\mapsto 6\mapsto 7\mapsto 7),(2\mapsto 6\mapsto 8\mapsto 8),(2\mapsto 6\mapsto 9\mapsto 9),(2\mapsto 7\mapsto 1\mapsto 1),(2\mapsto 7\mapsto 2\mapsto 2),(2\mapsto 7\mapsto 3\mapsto 3),(2\mapsto 7\mapsto 4\mapsto 4),(2\mapsto 7\mapsto 5\mapsto 5),(2\mapsto 7\mapsto 6\mapsto 6),(2\mapsto 7\mapsto 7\mapsto 7),(2\mapsto 7\mapsto 8\mapsto 8),(2\mapsto 7\mapsto 9\mapsto 9),(2\mapsto 8\mapsto 1\mapsto 1),(2\mapsto 8\mapsto 2\mapsto 2),(2\mapsto 8\mapsto 3\mapsto 3),(2\mapsto 8\mapsto 4\mapsto 4),(2\mapsto 8\mapsto 5\mapsto 5),(2\mapsto 8\mapsto 6\mapsto 6),(2\mapsto 8\mapsto 7\mapsto 7),(2\mapsto 8\mapsto 8\mapsto 8),(2\mapsto 8\mapsto 9\mapsto 9),(2\mapsto 9\mapsto 1\mapsto 1),(2\mapsto 9\mapsto 2\mapsto 2),(2\mapsto 9\mapsto 3\mapsto 3),(2\mapsto 9\mapsto 4\mapsto 4),(2\mapsto 9\mapsto 5\mapsto 5),(2\mapsto 9\mapsto 6\mapsto 6),(2\mapsto 9\mapsto 7\mapsto 7),(2\mapsto 9\mapsto 8\mapsto 8),(2\mapsto 9\mapsto 9\mapsto 9),(3\mapsto 4\mapsto 1\mapsto 1),(3\mapsto 4\mapsto 2\mapsto 2),(3\mapsto 4\mapsto 3\mapsto 3),(3\mapsto 4\mapsto 4\mapsto 4),(3\mapsto 4\mapsto 5\mapsto 5),(3\mapsto 4\mapsto 6\mapsto 6),(3\mapsto 4\mapsto 7\mapsto 7),(3\mapsto 4\mapsto 8\mapsto 8),(3\mapsto 4\mapsto 9\mapsto 9),(3\mapsto 5\mapsto 1\mapsto 1),(3\mapsto 5\mapsto 2\mapsto 2),(3\mapsto 5\mapsto 3\mapsto 3),(3\mapsto 5\mapsto 4\mapsto 4),(3\mapsto 5\mapsto 5\mapsto 5),(3\mapsto 5\mapsto 6\mapsto 6),(3\mapsto 5\mapsto 7\mapsto 7),(3\mapsto 5\mapsto 8\mapsto 8),(3\mapsto 5\mapsto 9\mapsto 9),(3\mapsto 6\mapsto 1\mapsto 1),(3\mapsto 6\mapsto 2\mapsto 2),(3\mapsto 6\mapsto 3\mapsto 3),(3\mapsto 6\mapsto 4\mapsto 4),(3\mapsto 6\mapsto 5\mapsto 5),(3\mapsto 6\mapsto 6\mapsto 6),(3\mapsto 6\mapsto 7\mapsto 7),(3\mapsto 6\mapsto 8\mapsto 8),(3\mapsto 6\mapsto 9\mapsto 9),(3\mapsto 7\mapsto 1\mapsto 1),(3\mapsto 7\mapsto 2\mapsto 2),(3\mapsto 7\mapsto 3\mapsto 3),(3\mapsto 7\mapsto 4\mapsto 4),(3\mapsto 7\mapsto 5\mapsto 5),(3\mapsto 7\mapsto 6\mapsto 6),(3\mapsto 7\mapsto 7\mapsto 7),(3\mapsto 7\mapsto 8\mapsto 8),(3\mapsto 7\mapsto 9\mapsto 9),(3\mapsto 8\mapsto 1\mapsto 1),(3\mapsto 8\mapsto 2\mapsto 2),(3\mapsto 8\mapsto 3\mapsto 3),(3\mapsto 8\mapsto 4\mapsto 4),(3\mapsto 8\mapsto 5\mapsto 5),(3\mapsto 8\mapsto 6\mapsto 6),(3\mapsto 8\mapsto 7\mapsto 7),(3\mapsto 8\mapsto 8\mapsto 8),(3\mapsto 8\mapsto 9\mapsto 9),(3\mapsto 9\mapsto 1\mapsto 1),(3\mapsto 9\mapsto 2\mapsto 2),(3\mapsto 9\mapsto 3\mapsto 3),(3\mapsto 9\mapsto 4\mapsto 4),(3\mapsto 9\mapsto 5\mapsto 5),(3\mapsto 9\mapsto 6\mapsto 6),(3\mapsto 9\mapsto 7\mapsto 7),(3\mapsto 9\mapsto 8\mapsto 8),(3\mapsto 9\mapsto 9\mapsto 9),(4\mapsto 5\mapsto 1\mapsto 1),(4\mapsto 5\mapsto 2\mapsto 2),(4\mapsto 5\mapsto 3\mapsto 3),(4\mapsto 5\mapsto 4\mapsto 4),(4\mapsto 5\mapsto 5\mapsto 5),(4\mapsto 5\mapsto 6\mapsto 6),(4\mapsto 5\mapsto 7\mapsto 7),(4\mapsto 5\mapsto 8\mapsto 8),(4\mapsto 5\mapsto 9\mapsto 9),(4\mapsto 6\mapsto 1\mapsto 1),(4\mapsto 6\mapsto 2\mapsto 2),(4\mapsto 6\mapsto 3\mapsto 3),(4\mapsto 6\mapsto 4\mapsto 4),(4\mapsto 6\mapsto 5\mapsto 5),(4\mapsto 6\mapsto 6\mapsto 6),(4\mapsto 6\mapsto 7\mapsto 7),(4\mapsto 6\mapsto 8\mapsto 8),(4\mapsto 6\mapsto 9\mapsto 9),(4\mapsto 7\mapsto 1\mapsto 1),(4\mapsto 7\mapsto 2\mapsto 2),(4\mapsto 7\mapsto 3\mapsto 3),(4\mapsto 7\mapsto 4\mapsto 4),(4\mapsto 7\mapsto 5\mapsto 5),(4\mapsto 7\mapsto 6\mapsto 6),(4\mapsto 7\mapsto 7\mapsto 7),(4\mapsto 7\mapsto 8\mapsto 8),(4\mapsto 7\mapsto 9\mapsto 9),(4\mapsto 8\mapsto 1\mapsto 1),(4\mapsto 8\mapsto 2\mapsto 2),(4\mapsto 8\mapsto 3\mapsto 3),(4\mapsto 8\mapsto 4\mapsto 4),(4\mapsto 8\mapsto 5\mapsto 5),(4\mapsto 8\mapsto 6\mapsto 6),(4\mapsto 8\mapsto 7\mapsto 7),(4\mapsto 8\mapsto 8\mapsto 8),(4\mapsto 8\mapsto 9\mapsto 9),(4\mapsto 9\mapsto 1\mapsto 1),(4\mapsto 9\mapsto 2\mapsto 2),(4\mapsto 9\mapsto 3\mapsto 3),(4\mapsto 9\mapsto 4\mapsto 4),(4\mapsto 9\mapsto 5\mapsto 5),(4\mapsto 9\mapsto 6\mapsto 6),(4\mapsto 9\mapsto 7\mapsto 7),(4\mapsto 9\mapsto 8\mapsto 8),(4\mapsto 9\mapsto 9\mapsto 9),(5\mapsto 6\mapsto 1\mapsto 1),(5\mapsto 6\mapsto 2\mapsto 2),(5\mapsto 6\mapsto 3\mapsto 3),(5\mapsto 6\mapsto 4\mapsto 4),(5\mapsto 6\mapsto 5\mapsto 5),(5\mapsto 6\mapsto 6\mapsto 6),(5\mapsto 6\mapsto 7\mapsto 7),(5\mapsto 6\mapsto 8\mapsto 8),(5\mapsto 6\mapsto 9\mapsto 9),(5\mapsto 7\mapsto 1\mapsto 1),(5\mapsto 7\mapsto 2\mapsto 2),(5\mapsto 7\mapsto 3\mapsto 3),(5\mapsto 7\mapsto 4\mapsto 4),(5\mapsto 7\mapsto 5\mapsto 5),(5\mapsto 7\mapsto 6\mapsto 6),(5\mapsto 7\mapsto 7\mapsto 7),(5\mapsto 7\mapsto 8\mapsto 8),(5\mapsto 7\mapsto 9\mapsto 9),(5\mapsto 8\mapsto 1\mapsto 1),(5\mapsto 8\mapsto 2\mapsto 2),(5\mapsto 8\mapsto 3\mapsto 3),(5\mapsto 8\mapsto 4\mapsto 4),(5\mapsto 8\mapsto 5\mapsto 5),(5\mapsto 8\mapsto 6\mapsto 6),(5\mapsto 8\mapsto 7\mapsto 7),(5\mapsto 8\mapsto 8\mapsto 8),(5\mapsto 8\mapsto 9\mapsto 9),(5\mapsto 9\mapsto 1\mapsto 1),(5\mapsto 9\mapsto 2\mapsto 2),(5\mapsto 9\mapsto 3\mapsto 3),(5\mapsto 9\mapsto 4\mapsto 4),(5\mapsto 9\mapsto 5\mapsto 5),(5\mapsto 9\mapsto 6\mapsto 6),(5\mapsto 9\mapsto 7\mapsto 7),(5\mapsto 9\mapsto 8\mapsto 8),(5\mapsto 9\mapsto 9\mapsto 9),(6\mapsto 7\mapsto 1\mapsto 1),(6\mapsto 7\mapsto 2\mapsto 2),(6\mapsto 7\mapsto 3\mapsto 3),(6\mapsto 7\mapsto 4\mapsto 4),(6\mapsto 7\mapsto 5\mapsto 5),(6\mapsto 7\mapsto 6\mapsto 6),(6\mapsto 7\mapsto 7\mapsto 7),(6\mapsto 7\mapsto 8\mapsto 8),(6\mapsto 7\mapsto 9\mapsto 9),(6\mapsto 8\mapsto 1\mapsto 1),(6\mapsto 8\mapsto 2\mapsto 2),(6\mapsto 8\mapsto 3\mapsto 3),(6\mapsto 8\mapsto 4\mapsto 4),(6\mapsto 8\mapsto 5\mapsto 5),(6\mapsto 8\mapsto 6\mapsto 6),(6\mapsto 8\mapsto 7\mapsto 7),(6\mapsto 8\mapsto 8\mapsto 8),(6\mapsto 8\mapsto 9\mapsto 9),(6\mapsto 9\mapsto 1\mapsto 1),(6\mapsto 9\mapsto 2\mapsto 2),(6\mapsto 9\mapsto 3\mapsto 3),(6\mapsto 9\mapsto 4\mapsto 4),(6\mapsto 9\mapsto 5\mapsto 5),(6\mapsto 9\mapsto 6\mapsto 6),(6\mapsto 9\mapsto 7\mapsto 7),(6\mapsto 9\mapsto 8\mapsto 8),(6\mapsto 9\mapsto 9\mapsto 9),(7\mapsto 8\mapsto 1\mapsto 1),(7\mapsto 8\mapsto 2\mapsto 2),(7\mapsto 8\mapsto 3\mapsto 3),(7\mapsto 8\mapsto 4\mapsto 4),(7\mapsto 8\mapsto 5\mapsto 5),(7\mapsto 8\mapsto 6\mapsto 6),(7\mapsto 8\mapsto 7\mapsto 7),(7\mapsto 8\mapsto 8\mapsto 8),(7\mapsto 8\mapsto 9\mapsto 9),(7\mapsto 9\mapsto 1\mapsto 1),(7\mapsto 9\mapsto 2\mapsto 2),(7\mapsto 9\mapsto 3\mapsto 3),(7\mapsto 9\mapsto 4\mapsto 4),(7\mapsto 9\mapsto 5\mapsto 5),(7\mapsto 9\mapsto 6\mapsto 6),(7\mapsto 9\mapsto 7\mapsto 7),(7\mapsto 9\mapsto 8\mapsto 8),(7\mapsto 9\mapsto 9\mapsto 9),(8\mapsto 9\mapsto 1\mapsto 1),(8\mapsto 9\mapsto 2\mapsto 2),(8\mapsto 9\mapsto 3\mapsto 3),(8\mapsto 9\mapsto 4\mapsto 4),(8\mapsto 9\mapsto 5\mapsto 5),(8\mapsto 9\mapsto 6\mapsto 6),(8\mapsto 9\mapsto 7\mapsto 7),(8\mapsto 9\mapsto 8\mapsto 8),(8\mapsto 9\mapsto 9\mapsto 9)\}$
* $\mathit{Diff} = \emptyset$
* $\mathit{SUBSQ} = \{\{1,2,3\},\{4,5,6\},\{7,8,9\}\}$
TRUE
Solution:
Diff3 = {(1↦1↦2↦1),(1↦1↦3↦1),(1↦1↦3↦2),(1↦1↦5↦4),(1↦1↦6↦4),(1↦1↦6↦5),(1↦1↦8↦7),(1↦1↦9↦7),(1↦1↦9↦8),(2↦1↦1↦1),(2↦1↦1↦2),(2↦1↦1↦3),(2↦1↦2↦1),(2↦1↦2↦2),(2↦1↦2↦3),(2↦1↦3↦1),(2↦1↦3↦2),(2↦1↦3↦3),(2↦1↦4↦4),(2↦1↦4↦5),(2↦1↦4↦6),(2↦1↦5↦4),(2↦1↦5↦5),(2↦1↦5↦6),(2↦1↦6↦4),(2↦1↦6↦5),(2↦1↦6↦6),(2↦1↦7↦7),(2↦1↦7↦8),(2↦1↦7↦9),(2↦1↦8↦7),(2↦1↦8↦8),(2↦1↦8↦9),(2↦1↦9↦7),(2↦1↦9↦8),(2↦1↦9↦9),(2↦2↦2↦1),(2↦2↦3↦1),(2↦2↦3↦2),(2↦2↦5↦4),(2↦2↦6↦4),(2↦2↦6↦5),(2↦2↦8↦7),(2↦2↦9↦7),(2↦2↦9↦8),(3↦1↦1↦1),(3↦1↦1↦2),(3↦1↦1↦3),(3↦1↦2↦1),(3↦1↦2↦2),(3↦1↦2↦3),(3↦1↦3↦1),(3↦1↦3↦2),(3↦1↦3↦3),(3↦1↦4↦4),(3↦1↦4↦5),(3↦1↦4↦6),(3↦1↦5↦4),(3↦1↦5↦5),(3↦1↦5↦6),(3↦1↦6↦4),(3↦1↦6↦5),(3↦1↦6↦6),(3↦1↦7↦7),(3↦1↦7↦8),(3↦1↦7↦9),(3↦1↦8↦7),(3↦1↦8↦8),(3↦1↦8↦9),(3↦1↦9↦7),(3↦1↦9↦8),(3↦1↦9↦9),(3↦2↦1↦1),(3↦2↦1↦2),(3↦2↦1↦3),(3↦2↦2↦1),(3↦2↦2↦2),(3↦2↦2↦3),(3↦2↦3↦1),(3↦2↦3↦2),(3↦2↦3↦3),(3↦2↦4↦4),(3↦2↦4↦5),(3↦2↦4↦6),(3↦2↦5↦4),(3↦2↦5↦5),(3↦2↦5↦6),(3↦2↦6↦4),(3↦2↦6↦5),(3↦2↦6↦6),(3↦2↦7↦7),(3↦2↦7↦8),(3↦2↦7↦9),(3↦2↦8↦7),(3↦2↦8↦8),(3↦2↦8↦9),(3↦2↦9↦7),(3↦2↦9↦8),(3↦2↦9↦9),(3↦3↦2↦1),(3↦3↦3↦1),(3↦3↦3↦2),(3↦3↦5↦4),(3↦3↦6↦4),(3↦3↦6↦5),(3↦3↦8↦7),(3↦3↦9↦7),(3↦3↦9↦8),(4↦4↦2↦1),(4↦4↦3↦1),(4↦4↦3↦2),(4↦4↦5↦4),(4↦4↦6↦4),(4↦4↦6↦5),(4↦4↦8↦7),(4↦4↦9↦7),(4↦4↦9↦8),(5↦4↦1↦1),(5↦4↦1↦2),(5↦4↦1↦3),(5↦4↦2↦1),(5↦4↦2↦2),(5↦4↦2↦3),(5↦4↦3↦1),(5↦4↦3↦2),(5↦4↦3↦3),(5↦4↦4↦4),(5↦4↦4↦5),(5↦4↦4↦6),(5↦4↦5↦4),(5↦4↦5↦5),(5↦4↦5↦6),(5↦4↦6↦4),(5↦4↦6↦5),(5↦4↦6↦6),(5↦4↦7↦7),(5↦4↦7↦8),(5↦4↦7↦9),(5↦4↦8↦7),(5↦4↦8↦8),(5↦4↦8↦9),(5↦4↦9↦7),(5↦4↦9↦8),(5↦4↦9↦9),(5↦5↦2↦1),(5↦5↦3↦1),(5↦5↦3↦2),(5↦5↦5↦4),(5↦5↦6↦4),(5↦5↦6↦5),(5↦5↦8↦7),(5↦5↦9↦7),(5↦5↦9↦8),(6↦4↦1↦1),(6↦4↦1↦2),(6↦4↦1↦3),(6↦4↦2↦1),(6↦4↦2↦2),(6↦4↦2↦3),(6↦4↦3↦1),(6↦4↦3↦2),(6↦4↦3↦3),(6↦4↦4↦4),(6↦4↦4↦5),(6↦4↦4↦6),(6↦4↦5↦4),(6↦4↦5↦5),(6↦4↦5↦6),(6↦4↦6↦4),(6↦4↦6↦5),(6↦4↦6↦6),(6↦4↦7↦7),(6↦4↦7↦8),(6↦4↦7↦9),(6↦4↦8↦7),(6↦4↦8↦8),(6↦4↦8↦9),(6↦4↦9↦7),(6↦4↦9↦8),(6↦4↦9↦9),(6↦5↦1↦1),(6↦5↦1↦2),(6↦5↦1↦3),(6↦5↦2↦1),(6↦5↦2↦2),(6↦5↦2↦3),(6↦5↦3↦1),(6↦5↦3↦2),(6↦5↦3↦3),(6↦5↦4↦4),(6↦5↦4↦5),(6↦5↦4↦6),(6↦5↦5↦4),(6↦5↦5↦5),(6↦5↦5↦6),(6↦5↦6↦4),(6↦5↦6↦5),(6↦5↦6↦6),(6↦5↦7↦7),(6↦5↦7↦8),(6↦5↦7↦9),(6↦5↦8↦7),(6↦5↦8↦8),(6↦5↦8↦9),(6↦5↦9↦7),(6↦5↦9↦8),(6↦5↦9↦9),(6↦6↦2↦1),(6↦6↦3↦1),(6↦6↦3↦2),(6↦6↦5↦4),(6↦6↦6↦4),(6↦6↦6↦5),(6↦6↦8↦7),(6↦6↦9↦7),(6↦6↦9↦8),(7↦7↦2↦1),(7↦7↦3↦1),(7↦7↦3↦2),(7↦7↦5↦4),(7↦7↦6↦4),(7↦7↦6↦5),(7↦7↦8↦7),(7↦7↦9↦7),(7↦7↦9↦8),(8↦7↦1↦1),(8↦7↦1↦2),(8↦7↦1↦3),(8↦7↦2↦1),(8↦7↦2↦2),(8↦7↦2↦3),(8↦7↦3↦1),(8↦7↦3↦2),(8↦7↦3↦3),(8↦7↦4↦4),(8↦7↦4↦5),(8↦7↦4↦6),(8↦7↦5↦4),(8↦7↦5↦5),(8↦7↦5↦6),(8↦7↦6↦4),(8↦7↦6↦5),(8↦7↦6↦6),(8↦7↦7↦7),(8↦7↦7↦8),(8↦7↦7↦9),(8↦7↦8↦7),(8↦7↦8↦8),(8↦7↦8↦9),(8↦7↦9↦7),(8↦7↦9↦8),(8↦7↦9↦9),(8↦8↦2↦1),(8↦8↦3↦1),(8↦8↦3↦2),(8↦8↦5↦4),(8↦8↦6↦4),(8↦8↦6↦5),(8↦8↦8↦7),(8↦8↦9↦7),(8↦8↦9↦8),(9↦7↦1↦1),(9↦7↦1↦2),(9↦7↦1↦3),(9↦7↦2↦1),(9↦7↦2↦2),(9↦7↦2↦3),(9↦7↦3↦1),(9↦7↦3↦2),(9↦7↦3↦3),(9↦7↦4↦4),(9↦7↦4↦5),(9↦7↦4↦6),(9↦7↦5↦4),(9↦7↦5↦5),(9↦7↦5↦6),(9↦7↦6↦4),(9↦7↦6↦5),(9↦7↦6↦6),(9↦7↦7↦7),(9↦7↦7↦8),(9↦7↦7↦9),(9↦7↦8↦7),(9↦7↦8↦8),(9↦7↦8↦9),(9↦7↦9↦7),(9↦7↦9↦8),(9↦7↦9↦9),(9↦8↦1↦1),(9↦8↦1↦2),(9↦8↦1↦3),(9↦8↦2↦1),(9↦8↦2↦2),(9↦8↦2↦3),(9↦8↦3↦1),(9↦8↦3↦2),(9↦8↦3↦3),(9↦8↦4↦4),(9↦8↦4↦5),(9↦8↦4↦6),(9↦8↦5↦4),(9↦8↦5↦5),(9↦8↦5↦6),(9↦8↦6↦4),(9↦8↦6↦5),(9↦8↦6↦6),(9↦8↦7↦7),(9↦8↦7↦8),(9↦8↦7↦9),(9↦8↦8↦7),(9↦8↦8↦8),(9↦8↦8↦9),(9↦8↦9↦7),(9↦8↦9↦8),(9↦8↦9↦9),(9↦9↦2↦1),(9↦9↦3↦1),(9↦9↦3↦2),(9↦9↦5↦4),(9↦9↦6↦4),(9↦9↦6↦5),(9↦9↦8↦7),(9↦9↦9↦7),(9↦9↦9↦8)}
Diff2 = {(1↦1↦1↦2),(1↦1↦1↦3),(1↦1↦1↦4),(1↦1↦1↦5),(1↦1↦1↦6),(1↦1↦1↦7),(1↦1↦1↦8),(1↦1↦1↦9),(1↦1↦2↦3),(1↦1↦2↦4),(1↦1↦2↦5),(1↦1↦2↦6),(1↦1↦2↦7),(1↦1↦2↦8),(1↦1↦2↦9),(1↦1↦3↦4),(1↦1↦3↦5),(1↦1↦3↦6),(1↦1↦3↦7),(1↦1↦3↦8),(1↦1↦3↦9),(1↦1↦4↦5),(1↦1↦4↦6),(1↦1↦4↦7),(1↦1↦4↦8),(1↦1↦4↦9),(1↦1↦5↦6),(1↦1↦5↦7),(1↦1↦5↦8),(1↦1↦5↦9),(1↦1↦6↦7),(1↦1↦6↦8),(1↦1↦6↦9),(1↦1↦7↦8),(1↦1↦7↦9),(1↦1↦8↦9),(2↦2↦1↦2),(2↦2↦1↦3),(2↦2↦1↦4),(2↦2↦1↦5),(2↦2↦1↦6),(2↦2↦1↦7),(2↦2↦1↦8),(2↦2↦1↦9),(2↦2↦2↦3),(2↦2↦2↦4),(2↦2↦2↦5),(2↦2↦2↦6),(2↦2↦2↦7),(2↦2↦2↦8),(2↦2↦2↦9),(2↦2↦3↦4),(2↦2↦3↦5),(2↦2↦3↦6),(2↦2↦3↦7),(2↦2↦3↦8),(2↦2↦3↦9),(2↦2↦4↦5),(2↦2↦4↦6),(2↦2↦4↦7),(2↦2↦4↦8),(2↦2↦4↦9),(2↦2↦5↦6),(2↦2↦5↦7),(2↦2↦5↦8),(2↦2↦5↦9),(2↦2↦6↦7),(2↦2↦6↦8),(2↦2↦6↦9),(2↦2↦7↦8),(2↦2↦7↦9),(2↦2↦8↦9),(3↦3↦1↦2),(3↦3↦1↦3),(3↦3↦1↦4),(3↦3↦1↦5),(3↦3↦1↦6),(3↦3↦1↦7),(3↦3↦1↦8),(3↦3↦1↦9),(3↦3↦2↦3),(3↦3↦2↦4),(3↦3↦2↦5),(3↦3↦2↦6),(3↦3↦2↦7),(3↦3↦2↦8),(3↦3↦2↦9),(3↦3↦3↦4),(3↦3↦3↦5),(3↦3↦3↦6),(3↦3↦3↦7),(3↦3↦3↦8),(3↦3↦3↦9),(3↦3↦4↦5),(3↦3↦4↦6),(3↦3↦4↦7),(3↦3↦4↦8),(3↦3↦4↦9),(3↦3↦5↦6),(3↦3↦5↦7),(3↦3↦5↦8),(3↦3↦5↦9),(3↦3↦6↦7),(3↦3↦6↦8),(3↦3↦6↦9),(3↦3↦7↦8),(3↦3↦7↦9),(3↦3↦8↦9),(4↦4↦1↦2),(4↦4↦1↦3),(4↦4↦1↦4),(4↦4↦1↦5),(4↦4↦1↦6),(4↦4↦1↦7),(4↦4↦1↦8),(4↦4↦1↦9),(4↦4↦2↦3),(4↦4↦2↦4),(4↦4↦2↦5),(4↦4↦2↦6),(4↦4↦2↦7),(4↦4↦2↦8),(4↦4↦2↦9),(4↦4↦3↦4),(4↦4↦3↦5),(4↦4↦3↦6),(4↦4↦3↦7),(4↦4↦3↦8),(4↦4↦3↦9),(4↦4↦4↦5),(4↦4↦4↦6),(4↦4↦4↦7),(4↦4↦4↦8),(4↦4↦4↦9),(4↦4↦5↦6),(4↦4↦5↦7),(4↦4↦5↦8),(4↦4↦5↦9),(4↦4↦6↦7),(4↦4↦6↦8),(4↦4↦6↦9),(4↦4↦7↦8),(4↦4↦7↦9),(4↦4↦8↦9),(5↦5↦1↦2),(5↦5↦1↦3),(5↦5↦1↦4),(5↦5↦1↦5),(5↦5↦1↦6),(5↦5↦1↦7),(5↦5↦1↦8),(5↦5↦1↦9),(5↦5↦2↦3),(5↦5↦2↦4),(5↦5↦2↦5),(5↦5↦2↦6),(5↦5↦2↦7),(5↦5↦2↦8),(5↦5↦2↦9),(5↦5↦3↦4),(5↦5↦3↦5),(5↦5↦3↦6),(5↦5↦3↦7),(5↦5↦3↦8),(5↦5↦3↦9),(5↦5↦4↦5),(5↦5↦4↦6),(5↦5↦4↦7),(5↦5↦4↦8),(5↦5↦4↦9),(5↦5↦5↦6),(5↦5↦5↦7),(5↦5↦5↦8),(5↦5↦5↦9),(5↦5↦6↦7),(5↦5↦6↦8),(5↦5↦6↦9),(5↦5↦7↦8),(5↦5↦7↦9),(5↦5↦8↦9),(6↦6↦1↦2),(6↦6↦1↦3),(6↦6↦1↦4),(6↦6↦1↦5),(6↦6↦1↦6),(6↦6↦1↦7),(6↦6↦1↦8),(6↦6↦1↦9),(6↦6↦2↦3),(6↦6↦2↦4),(6↦6↦2↦5),(6↦6↦2↦6),(6↦6↦2↦7),(6↦6↦2↦8),(6↦6↦2↦9),(6↦6↦3↦4),(6↦6↦3↦5),(6↦6↦3↦6),(6↦6↦3↦7),(6↦6↦3↦8),(6↦6↦3↦9),(6↦6↦4↦5),(6↦6↦4↦6),(6↦6↦4↦7),(6↦6↦4↦8),(6↦6↦4↦9),(6↦6↦5↦6),(6↦6↦5↦7),(6↦6↦5↦8),(6↦6↦5↦9),(6↦6↦6↦7),(6↦6↦6↦8),(6↦6↦6↦9),(6↦6↦7↦8),(6↦6↦7↦9),(6↦6↦8↦9),(7↦7↦1↦2),(7↦7↦1↦3),(7↦7↦1↦4),(7↦7↦1↦5),(7↦7↦1↦6),(7↦7↦1↦7),(7↦7↦1↦8),(7↦7↦1↦9),(7↦7↦2↦3),(7↦7↦2↦4),(7↦7↦2↦5),(7↦7↦2↦6),(7↦7↦2↦7),(7↦7↦2↦8),(7↦7↦2↦9),(7↦7↦3↦4),(7↦7↦3↦5),(7↦7↦3↦6),(7↦7↦3↦7),(7↦7↦3↦8),(7↦7↦3↦9),(7↦7↦4↦5),(7↦7↦4↦6),(7↦7↦4↦7),(7↦7↦4↦8),(7↦7↦4↦9),(7↦7↦5↦6),(7↦7↦5↦7),(7↦7↦5↦8),(7↦7↦5↦9),(7↦7↦6↦7),(7↦7↦6↦8),(7↦7↦6↦9),(7↦7↦7↦8),(7↦7↦7↦9),(7↦7↦8↦9),(8↦8↦1↦2),(8↦8↦1↦3),(8↦8↦1↦4),(8↦8↦1↦5),(8↦8↦1↦6),(8↦8↦1↦7),(8↦8↦1↦8),(8↦8↦1↦9),(8↦8↦2↦3),(8↦8↦2↦4),(8↦8↦2↦5),(8↦8↦2↦6),(8↦8↦2↦7),(8↦8↦2↦8),(8↦8↦2↦9),(8↦8↦3↦4),(8↦8↦3↦5),(8↦8↦3↦6),(8↦8↦3↦7),(8↦8↦3↦8),(8↦8↦3↦9),(8↦8↦4↦5),(8↦8↦4↦6),(8↦8↦4↦7),(8↦8↦4↦8),(8↦8↦4↦9),(8↦8↦5↦6),(8↦8↦5↦7),(8↦8↦5↦8),(8↦8↦5↦9),(8↦8↦6↦7),(8↦8↦6↦8),(8↦8↦6↦9),(8↦8↦7↦8),(8↦8↦7↦9),(8↦8↦8↦9),(9↦9↦1↦2),(9↦9↦1↦3),(9↦9↦1↦4),(9↦9↦1↦5),(9↦9↦1↦6),(9↦9↦1↦7),(9↦9↦1↦8),(9↦9↦1↦9),(9↦9↦2↦3),(9↦9↦2↦4),(9↦9↦2↦5),(9↦9↦2↦6),(9↦9↦2↦7),(9↦9↦2↦8),(9↦9↦2↦9),(9↦9↦3↦4),(9↦9↦3↦5),(9↦9↦3↦6),(9↦9↦3↦7),(9↦9↦3↦8),(9↦9↦3↦9),(9↦9↦4↦5),(9↦9↦4↦6),(9↦9↦4↦7),(9↦9↦4↦8),(9↦9↦4↦9),(9↦9↦5↦6),(9↦9↦5↦7),(9↦9↦5↦8),(9↦9↦5↦9),(9↦9↦6↦7),(9↦9↦6↦8),(9↦9↦6↦9),(9↦9↦7↦8),(9↦9↦7↦9),(9↦9↦8↦9)}
Board = {(1↦{(1↦1),(2↦1),(3↦1),(4↦1),(5↦1),(6↦1),(7↦1),(8↦1),(9↦1)}),(2↦{(1↦1),(2↦1),(3↦1),(4↦1),(5↦1),(6↦1),(7↦1),(8↦1),(9↦1)}),(3↦{(1↦1),(2↦1),(3↦1),(4↦1),(5↦1),(6↦1),(7↦1),(8↦1),(9↦1)}),(4↦{(1↦1),(2↦1),(3↦1),(4↦1),(5↦1),(6↦1),(7↦1),(8↦1),(9↦1)}),(5↦{(1↦1),(2↦1),(3↦1),(4↦1),(5↦1),(6↦1),(7↦1),(8↦1),(9↦1)}),(6↦{(1↦1),(2↦1),(3↦1),(4↦1),(5↦1),(6↦1),(7↦1),(8↦1),(9↦1)}),(7↦{(1↦1),(2↦1),(3↦1),(4↦1),(5↦1),(6↦1),(7↦1),(8↦1),(9↦1)}),(8↦{(1↦1),(2↦1),(3↦1),(4↦1),(5↦1),(6↦1),(7↦1),(8↦1),(9↦1)}),(9↦{(1↦1),(2↦1),(3↦1),(4↦1),(5↦1),(6↦1),(7↦1),(8↦1),(9↦1)})}
DOM = {1,2,3,4,5,6,7,8,9}
Diff1 = {(1↦2↦1↦1),(1↦2↦2↦2),(1↦2↦3↦3),(1↦2↦4↦4),(1↦2↦5↦5),(1↦2↦6↦6),(1↦2↦7↦7),(1↦2↦8↦8),(1↦2↦9↦9),(1↦3↦1↦1),(1↦3↦2↦2),(1↦3↦3↦3),(1↦3↦4↦4),(1↦3↦5↦5),(1↦3↦6↦6),(1↦3↦7↦7),(1↦3↦8↦8),(1↦3↦9↦9),(1↦4↦1↦1),(1↦4↦2↦2),(1↦4↦3↦3),(1↦4↦4↦4),(1↦4↦5↦5),(1↦4↦6↦6),(1↦4↦7↦7),(1↦4↦8↦8),(1↦4↦9↦9),(1↦5↦1↦1),(1↦5↦2↦2),(1↦5↦3↦3),(1↦5↦4↦4),(1↦5↦5↦5),(1↦5↦6↦6),(1↦5↦7↦7),(1↦5↦8↦8),(1↦5↦9↦9),(1↦6↦1↦1),(1↦6↦2↦2),(1↦6↦3↦3),(1↦6↦4↦4),(1↦6↦5↦5),(1↦6↦6↦6),(1↦6↦7↦7),(1↦6↦8↦8),(1↦6↦9↦9),(1↦7↦1↦1),(1↦7↦2↦2),(1↦7↦3↦3),(1↦7↦4↦4),(1↦7↦5↦5),(1↦7↦6↦6),(1↦7↦7↦7),(1↦7↦8↦8),(1↦7↦9↦9),(1↦8↦1↦1),(1↦8↦2↦2),(1↦8↦3↦3),(1↦8↦4↦4),(1↦8↦5↦5),(1↦8↦6↦6),(1↦8↦7↦7),(1↦8↦8↦8),(1↦8↦9↦9),(1↦9↦1↦1),(1↦9↦2↦2),(1↦9↦3↦3),(1↦9↦4↦4),(1↦9↦5↦5),(1↦9↦6↦6),(1↦9↦7↦7),(1↦9↦8↦8),(1↦9↦9↦9),(2↦3↦1↦1),(2↦3↦2↦2),(2↦3↦3↦3),(2↦3↦4↦4),(2↦3↦5↦5),(2↦3↦6↦6),(2↦3↦7↦7),(2↦3↦8↦8),(2↦3↦9↦9),(2↦4↦1↦1),(2↦4↦2↦2),(2↦4↦3↦3),(2↦4↦4↦4),(2↦4↦5↦5),(2↦4↦6↦6),(2↦4↦7↦7),(2↦4↦8↦8),(2↦4↦9↦9),(2↦5↦1↦1),(2↦5↦2↦2),(2↦5↦3↦3),(2↦5↦4↦4),(2↦5↦5↦5),(2↦5↦6↦6),(2↦5↦7↦7),(2↦5↦8↦8),(2↦5↦9↦9),(2↦6↦1↦1),(2↦6↦2↦2),(2↦6↦3↦3),(2↦6↦4↦4),(2↦6↦5↦5),(2↦6↦6↦6),(2↦6↦7↦7),(2↦6↦8↦8),(2↦6↦9↦9),(2↦7↦1↦1),(2↦7↦2↦2),(2↦7↦3↦3),(2↦7↦4↦4),(2↦7↦5↦5),(2↦7↦6↦6),(2↦7↦7↦7),(2↦7↦8↦8),(2↦7↦9↦9),(2↦8↦1↦1),(2↦8↦2↦2),(2↦8↦3↦3),(2↦8↦4↦4),(2↦8↦5↦5),(2↦8↦6↦6),(2↦8↦7↦7),(2↦8↦8↦8),(2↦8↦9↦9),(2↦9↦1↦1),(2↦9↦2↦2),(2↦9↦3↦3),(2↦9↦4↦4),(2↦9↦5↦5),(2↦9↦6↦6),(2↦9↦7↦7),(2↦9↦8↦8),(2↦9↦9↦9),(3↦4↦1↦1),(3↦4↦2↦2),(3↦4↦3↦3),(3↦4↦4↦4),(3↦4↦5↦5),(3↦4↦6↦6),(3↦4↦7↦7),(3↦4↦8↦8),(3↦4↦9↦9),(3↦5↦1↦1),(3↦5↦2↦2),(3↦5↦3↦3),(3↦5↦4↦4),(3↦5↦5↦5),(3↦5↦6↦6),(3↦5↦7↦7),(3↦5↦8↦8),(3↦5↦9↦9),(3↦6↦1↦1),(3↦6↦2↦2),(3↦6↦3↦3),(3↦6↦4↦4),(3↦6↦5↦5),(3↦6↦6↦6),(3↦6↦7↦7),(3↦6↦8↦8),(3↦6↦9↦9),(3↦7↦1↦1),(3↦7↦2↦2),(3↦7↦3↦3),(3↦7↦4↦4),(3↦7↦5↦5),(3↦7↦6↦6),(3↦7↦7↦7),(3↦7↦8↦8),(3↦7↦9↦9),(3↦8↦1↦1),(3↦8↦2↦2),(3↦8↦3↦3),(3↦8↦4↦4),(3↦8↦5↦5),(3↦8↦6↦6),(3↦8↦7↦7),(3↦8↦8↦8),(3↦8↦9↦9),(3↦9↦1↦1),(3↦9↦2↦2),(3↦9↦3↦3),(3↦9↦4↦4),(3↦9↦5↦5),(3↦9↦6↦6),(3↦9↦7↦7),(3↦9↦8↦8),(3↦9↦9↦9),(4↦5↦1↦1),(4↦5↦2↦2),(4↦5↦3↦3),(4↦5↦4↦4),(4↦5↦5↦5),(4↦5↦6↦6),(4↦5↦7↦7),(4↦5↦8↦8),(4↦5↦9↦9),(4↦6↦1↦1),(4↦6↦2↦2),(4↦6↦3↦3),(4↦6↦4↦4),(4↦6↦5↦5),(4↦6↦6↦6),(4↦6↦7↦7),(4↦6↦8↦8),(4↦6↦9↦9),(4↦7↦1↦1),(4↦7↦2↦2),(4↦7↦3↦3),(4↦7↦4↦4),(4↦7↦5↦5),(4↦7↦6↦6),(4↦7↦7↦7),(4↦7↦8↦8),(4↦7↦9↦9),(4↦8↦1↦1),(4↦8↦2↦2),(4↦8↦3↦3),(4↦8↦4↦4),(4↦8↦5↦5),(4↦8↦6↦6),(4↦8↦7↦7),(4↦8↦8↦8),(4↦8↦9↦9),(4↦9↦1↦1),(4↦9↦2↦2),(4↦9↦3↦3),(4↦9↦4↦4),(4↦9↦5↦5),(4↦9↦6↦6),(4↦9↦7↦7),(4↦9↦8↦8),(4↦9↦9↦9),(5↦6↦1↦1),(5↦6↦2↦2),(5↦6↦3↦3),(5↦6↦4↦4),(5↦6↦5↦5),(5↦6↦6↦6),(5↦6↦7↦7),(5↦6↦8↦8),(5↦6↦9↦9),(5↦7↦1↦1),(5↦7↦2↦2),(5↦7↦3↦3),(5↦7↦4↦4),(5↦7↦5↦5),(5↦7↦6↦6),(5↦7↦7↦7),(5↦7↦8↦8),(5↦7↦9↦9),(5↦8↦1↦1),(5↦8↦2↦2),(5↦8↦3↦3),(5↦8↦4↦4),(5↦8↦5↦5),(5↦8↦6↦6),(5↦8↦7↦7),(5↦8↦8↦8),(5↦8↦9↦9),(5↦9↦1↦1),(5↦9↦2↦2),(5↦9↦3↦3),(5↦9↦4↦4),(5↦9↦5↦5),(5↦9↦6↦6),(5↦9↦7↦7),(5↦9↦8↦8),(5↦9↦9↦9),(6↦7↦1↦1),(6↦7↦2↦2),(6↦7↦3↦3),(6↦7↦4↦4),(6↦7↦5↦5),(6↦7↦6↦6),(6↦7↦7↦7),(6↦7↦8↦8),(6↦7↦9↦9),(6↦8↦1↦1),(6↦8↦2↦2),(6↦8↦3↦3),(6↦8↦4↦4),(6↦8↦5↦5),(6↦8↦6↦6),(6↦8↦7↦7),(6↦8↦8↦8),(6↦8↦9↦9),(6↦9↦1↦1),(6↦9↦2↦2),(6↦9↦3↦3),(6↦9↦4↦4),(6↦9↦5↦5),(6↦9↦6↦6),(6↦9↦7↦7),(6↦9↦8↦8),(6↦9↦9↦9),(7↦8↦1↦1),(7↦8↦2↦2),(7↦8↦3↦3),(7↦8↦4↦4),(7↦8↦5↦5),(7↦8↦6↦6),(7↦8↦7↦7),(7↦8↦8↦8),(7↦8↦9↦9),(7↦9↦1↦1),(7↦9↦2↦2),(7↦9↦3↦3),(7↦9↦4↦4),(7↦9↦5↦5),(7↦9↦6↦6),(7↦9↦7↦7),(7↦9↦8↦8),(7↦9↦9↦9),(8↦9↦1↦1),(8↦9↦2↦2),(8↦9↦3↦3),(8↦9↦4↦4),(8↦9↦5↦5),(8↦9↦6↦6),(8↦9↦7↦7),(8↦9↦8↦8),(8↦9↦9↦9)}
Diff = ∅
SUBSQ = {{1,2,3},{4,5,6},{7,8,9}}
%% Cell type:markdown id: tags:
Let us now try and add some additional constraints for certain pre-established positions on the board, and put those into the variable P and require that the solution Board contains those values:
%% Cell type:code id: tags:
``` prob
:let P {(1,1,7), (1,2,8), (1,3,1), (2,1,9)}
```
%% Output
$\{(1\mapsto 1\mapsto 7),(1\mapsto 2\mapsto 8),(1\mapsto 3\mapsto 1),(2\mapsto 1\mapsto 9)\}$
{(1↦1↦7),(1↦2↦8),(1↦3↦1),(2↦1↦9)}
%% Cell type:markdown id: tags:
You can visualise the solution using the show command of the REPL:
%% Cell type:code id: tags:
``` prob
Board : DOM --> (DOM --> DOM) & !(x1,x2,y1,y2).((x1,x2,y1,y2):Diff => Board(x1)(y1) /= Board(x2)(y2)) & !(x,y,z).((x,y,z):P => Board(x)(y)=z)
```
%% Output
$\renewcommand{\emptyset}{\mathord\varnothing}\mathit{TRUE}$
**Solution:**
* $\mathit{P} = \{(1\mapsto 1\mapsto 7),(1\mapsto 2\mapsto 8),(1\mapsto 3\mapsto 1),(2\mapsto 1\mapsto 9)\}$
* $\mathit{Diff3} = \{(1\mapsto 1\mapsto 2\mapsto 1),(1\mapsto 1\mapsto 3\mapsto 1),(1\mapsto 1\mapsto 3\mapsto 2),(1\mapsto 1\mapsto 5\mapsto 4),(1\mapsto 1\mapsto 6\mapsto 4),(1\mapsto 1\mapsto 6\mapsto 5),(1\mapsto 1\mapsto 8\mapsto 7),(1\mapsto 1\mapsto 9\mapsto 7),(1\mapsto 1\mapsto 9\mapsto 8),(2\mapsto 1\mapsto 1\mapsto 1),(2\mapsto 1\mapsto 1\mapsto 2),(2\mapsto 1\mapsto 1\mapsto 3),(2\mapsto 1\mapsto 2\mapsto 1),(2\mapsto 1\mapsto 2\mapsto 2),(2\mapsto 1\mapsto 2\mapsto 3),(2\mapsto 1\mapsto 3\mapsto 1),(2\mapsto 1\mapsto 3\mapsto 2),(2\mapsto 1\mapsto 3\mapsto 3),(2\mapsto 1\mapsto 4\mapsto 4),(2\mapsto 1\mapsto 4\mapsto 5),(2\mapsto 1\mapsto 4\mapsto 6),(2\mapsto 1\mapsto 5\mapsto 4),(2\mapsto 1\mapsto 5\mapsto 5),(2\mapsto 1\mapsto 5\mapsto 6),(2\mapsto 1\mapsto 6\mapsto 4),(2\mapsto 1\mapsto 6\mapsto 5),(2\mapsto 1\mapsto 6\mapsto 6),(2\mapsto 1\mapsto 7\mapsto 7),(2\mapsto 1\mapsto 7\mapsto 8),(2\mapsto 1\mapsto 7\mapsto 9),(2\mapsto 1\mapsto 8\mapsto 7),(2\mapsto 1\mapsto 8\mapsto 8),(2\mapsto 1\mapsto 8\mapsto 9),(2\mapsto 1\mapsto 9\mapsto 7),(2\mapsto 1\mapsto 9\mapsto 8),(2\mapsto 1\mapsto 9\mapsto 9),(2\mapsto 2\mapsto 2\mapsto 1),(2\mapsto 2\mapsto 3\mapsto 1),(2\mapsto 2\mapsto 3\mapsto 2),(2\mapsto 2\mapsto 5\mapsto 4),(2\mapsto 2\mapsto 6\mapsto 4),(2\mapsto 2\mapsto 6\mapsto 5),(2\mapsto 2\mapsto 8\mapsto 7),(2\mapsto 2\mapsto 9\mapsto 7),(2\mapsto 2\mapsto 9\mapsto 8),(3\mapsto 1\mapsto 1\mapsto 1),(3\mapsto 1\mapsto 1\mapsto 2),(3\mapsto 1\mapsto 1\mapsto 3),(3\mapsto 1\mapsto 2\mapsto 1),(3\mapsto 1\mapsto 2\mapsto 2),(3\mapsto 1\mapsto 2\mapsto 3),(3\mapsto 1\mapsto 3\mapsto 1),(3\mapsto 1\mapsto 3\mapsto 2),(3\mapsto 1\mapsto 3\mapsto 3),(3\mapsto 1\mapsto 4\mapsto 4),(3\mapsto 1\mapsto 4\mapsto 5),(3\mapsto 1\mapsto 4\mapsto 6),(3\mapsto 1\mapsto 5\mapsto 4),(3\mapsto 1\mapsto 5\mapsto 5),(3\mapsto 1\mapsto 5\mapsto 6),(3\mapsto 1\mapsto 6\mapsto 4),(3\mapsto 1\mapsto 6\mapsto 5),(3\mapsto 1\mapsto 6\mapsto 6),(3\mapsto 1\mapsto 7\mapsto 7),(3\mapsto 1\mapsto 7\mapsto 8),(3\mapsto 1\mapsto 7\mapsto 9),(3\mapsto 1\mapsto 8\mapsto 7),(3\mapsto 1\mapsto 8\mapsto 8),(3\mapsto 1\mapsto 8\mapsto 9),(3\mapsto 1\mapsto 9\mapsto 7),(3\mapsto 1\mapsto 9\mapsto 8),(3\mapsto 1\mapsto 9\mapsto 9),(3\mapsto 2\mapsto 1\mapsto 1),(3\mapsto 2\mapsto 1\mapsto 2),(3\mapsto 2\mapsto 1\mapsto 3),(3\mapsto 2\mapsto 2\mapsto 1),(3\mapsto 2\mapsto 2\mapsto 2),(3\mapsto 2\mapsto 2\mapsto 3),(3\mapsto 2\mapsto 3\mapsto 1),(3\mapsto 2\mapsto 3\mapsto 2),(3\mapsto 2\mapsto 3\mapsto 3),(3\mapsto 2\mapsto 4\mapsto 4),(3\mapsto 2\mapsto 4\mapsto 5),(3\mapsto 2\mapsto 4\mapsto 6),(3\mapsto 2\mapsto 5\mapsto 4),(3\mapsto 2\mapsto 5\mapsto 5),(3\mapsto 2\mapsto 5\mapsto 6),(3\mapsto 2\mapsto 6\mapsto 4),(3\mapsto 2\mapsto 6\mapsto 5),(3\mapsto 2\mapsto 6\mapsto 6),(3\mapsto 2\mapsto 7\mapsto 7),(3\mapsto 2\mapsto 7\mapsto 8),(3\mapsto 2\mapsto 7\mapsto 9),(3\mapsto 2\mapsto 8\mapsto 7),(3\mapsto 2\mapsto 8\mapsto 8),(3\mapsto 2\mapsto 8\mapsto 9),(3\mapsto 2\mapsto 9\mapsto 7),(3\mapsto 2\mapsto 9\mapsto 8),(3\mapsto 2\mapsto 9\mapsto 9),(3\mapsto 3\mapsto 2\mapsto 1),(3\mapsto 3\mapsto 3\mapsto 1),(3\mapsto 3\mapsto 3\mapsto 2),(3\mapsto 3\mapsto 5\mapsto 4),(3\mapsto 3\mapsto 6\mapsto 4),(3\mapsto 3\mapsto 6\mapsto 5),(3\mapsto 3\mapsto 8\mapsto 7),(3\mapsto 3\mapsto 9\mapsto 7),(3\mapsto 3\mapsto 9\mapsto 8),(4\mapsto 4\mapsto 2\mapsto 1),(4\mapsto 4\mapsto 3\mapsto 1),(4\mapsto 4\mapsto 3\mapsto 2),(4\mapsto 4\mapsto 5\mapsto 4),(4\mapsto 4\mapsto 6\mapsto 4),(4\mapsto 4\mapsto 6\mapsto 5),(4\mapsto 4\mapsto 8\mapsto 7),(4\mapsto 4\mapsto 9\mapsto 7),(4\mapsto 4\mapsto 9\mapsto 8),(5\mapsto 4\mapsto 1\mapsto 1),(5\mapsto 4\mapsto 1\mapsto 2),(5\mapsto 4\mapsto 1\mapsto 3),(5\mapsto 4\mapsto 2\mapsto 1),(5\mapsto 4\mapsto 2\mapsto 2),(5\mapsto 4\mapsto 2\mapsto 3),(5\mapsto 4\mapsto 3\mapsto 1),(5\mapsto 4\mapsto 3\mapsto 2),(5\mapsto 4\mapsto 3\mapsto 3),(5\mapsto 4\mapsto 4\mapsto 4),(5\mapsto 4\mapsto 4\mapsto 5),(5\mapsto 4\mapsto 4\mapsto 6),(5\mapsto 4\mapsto 5\mapsto 4),(5\mapsto 4\mapsto 5\mapsto 5),(5\mapsto 4\mapsto 5\mapsto 6),(5\mapsto 4\mapsto 6\mapsto 4),(5\mapsto 4\mapsto 6\mapsto 5),(5\mapsto 4\mapsto 6\mapsto 6),(5\mapsto 4\mapsto 7\mapsto 7),(5\mapsto 4\mapsto 7\mapsto 8),(5\mapsto 4\mapsto 7\mapsto 9),(5\mapsto 4\mapsto 8\mapsto 7),(5\mapsto 4\mapsto 8\mapsto 8),(5\mapsto 4\mapsto 8\mapsto 9),(5\mapsto 4\mapsto 9\mapsto 7),(5\mapsto 4\mapsto 9\mapsto 8),(5\mapsto 4\mapsto 9\mapsto 9),(5\mapsto 5\mapsto 2\mapsto 1),(5\mapsto 5\mapsto 3\mapsto 1),(5\mapsto 5\mapsto 3\mapsto 2),(5\mapsto 5\mapsto 5\mapsto 4),(5\mapsto 5\mapsto 6\mapsto 4),(5\mapsto 5\mapsto 6\mapsto 5),(5\mapsto 5\mapsto 8\mapsto 7),(5\mapsto 5\mapsto 9\mapsto 7),(5\mapsto 5\mapsto 9\mapsto 8),(6\mapsto 4\mapsto 1\mapsto 1),(6\mapsto 4\mapsto 1\mapsto 2),(6\mapsto 4\mapsto 1\mapsto 3),(6\mapsto 4\mapsto 2\mapsto 1),(6\mapsto 4\mapsto 2\mapsto 2),(6\mapsto 4\mapsto 2\mapsto 3),(6\mapsto 4\mapsto 3\mapsto 1),(6\mapsto 4\mapsto 3\mapsto 2),(6\mapsto 4\mapsto 3\mapsto 3),(6\mapsto 4\mapsto 4\mapsto 4),(6\mapsto 4\mapsto 4\mapsto 5),(6\mapsto 4\mapsto 4\mapsto 6),(6\mapsto 4\mapsto 5\mapsto 4),(6\mapsto 4\mapsto 5\mapsto 5),(6\mapsto 4\mapsto 5\mapsto 6),(6\mapsto 4\mapsto 6\mapsto 4),(6\mapsto 4\mapsto 6\mapsto 5),(6\mapsto 4\mapsto 6\mapsto 6),(6\mapsto 4\mapsto 7\mapsto 7),(6\mapsto 4\mapsto 7\mapsto 8),(6\mapsto 4\mapsto 7\mapsto 9),(6\mapsto 4\mapsto 8\mapsto 7),(6\mapsto 4\mapsto 8\mapsto 8),(6\mapsto 4\mapsto 8\mapsto 9),(6\mapsto 4\mapsto 9\mapsto 7),(6\mapsto 4\mapsto 9\mapsto 8),(6\mapsto 4\mapsto 9\mapsto 9),(6\mapsto 5\mapsto 1\mapsto 1),(6\mapsto 5\mapsto 1\mapsto 2),(6\mapsto 5\mapsto 1\mapsto 3),(6\mapsto 5\mapsto 2\mapsto 1),(6\mapsto 5\mapsto 2\mapsto 2),(6\mapsto 5\mapsto 2\mapsto 3),(6\mapsto 5\mapsto 3\mapsto 1),(6\mapsto 5\mapsto 3\mapsto 2),(6\mapsto 5\mapsto 3\mapsto 3),(6\mapsto 5\mapsto 4\mapsto 4),(6\mapsto 5\mapsto 4\mapsto 5),(6\mapsto 5\mapsto 4\mapsto 6),(6\mapsto 5\mapsto 5\mapsto 4),(6\mapsto 5\mapsto 5\mapsto 5),(6\mapsto 5\mapsto 5\mapsto 6),(6\mapsto 5\mapsto 6\mapsto 4),(6\mapsto 5\mapsto 6\mapsto 5),(6\mapsto 5\mapsto 6\mapsto 6),(6\mapsto 5\mapsto 7\mapsto 7),(6\mapsto 5\mapsto 7\mapsto 8),(6\mapsto 5\mapsto 7\mapsto 9),(6\mapsto 5\mapsto 8\mapsto 7),(6\mapsto 5\mapsto 8\mapsto 8),(6\mapsto 5\mapsto 8\mapsto 9),(6\mapsto 5\mapsto 9\mapsto 7),(6\mapsto 5\mapsto 9\mapsto 8),(6\mapsto 5\mapsto 9\mapsto 9),(6\mapsto 6\mapsto 2\mapsto 1),(6\mapsto 6\mapsto 3\mapsto 1),(6\mapsto 6\mapsto 3\mapsto 2),(6\mapsto 6\mapsto 5\mapsto 4),(6\mapsto 6\mapsto 6\mapsto 4),(6\mapsto 6\mapsto 6\mapsto 5),(6\mapsto 6\mapsto 8\mapsto 7),(6\mapsto 6\mapsto 9\mapsto 7),(6\mapsto 6\mapsto 9\mapsto 8),(7\mapsto 7\mapsto 2\mapsto 1),(7\mapsto 7\mapsto 3\mapsto 1),(7\mapsto 7\mapsto 3\mapsto 2),(7\mapsto 7\mapsto 5\mapsto 4),(7\mapsto 7\mapsto 6\mapsto 4),(7\mapsto 7\mapsto 6\mapsto 5),(7\mapsto 7\mapsto 8\mapsto 7),(7\mapsto 7\mapsto 9\mapsto 7),(7\mapsto 7\mapsto 9\mapsto 8),(8\mapsto 7\mapsto 1\mapsto 1),(8\mapsto 7\mapsto 1\mapsto 2),(8\mapsto 7\mapsto 1\mapsto 3),(8\mapsto 7\mapsto 2\mapsto 1),(8\mapsto 7\mapsto 2\mapsto 2),(8\mapsto 7\mapsto 2\mapsto 3),(8\mapsto 7\mapsto 3\mapsto 1),(8\mapsto 7\mapsto 3\mapsto 2),(8\mapsto 7\mapsto 3\mapsto 3),(8\mapsto 7\mapsto 4\mapsto 4),(8\mapsto 7\mapsto 4\mapsto 5),(8\mapsto 7\mapsto 4\mapsto 6),(8\mapsto 7\mapsto 5\mapsto 4),(8\mapsto 7\mapsto 5\mapsto 5),(8\mapsto 7\mapsto 5\mapsto 6),(8\mapsto 7\mapsto 6\mapsto 4),(8\mapsto 7\mapsto 6\mapsto 5),(8\mapsto 7\mapsto 6\mapsto 6),(8\mapsto 7\mapsto 7\mapsto 7),(8\mapsto 7\mapsto 7\mapsto 8),(8\mapsto 7\mapsto 7\mapsto 9),(8\mapsto 7\mapsto 8\mapsto 7),(8\mapsto 7\mapsto 8\mapsto 8),(8\mapsto 7\mapsto 8\mapsto 9),(8\mapsto 7\mapsto 9\mapsto 7),(8\mapsto 7\mapsto 9\mapsto 8),(8\mapsto 7\mapsto 9\mapsto 9),(8\mapsto 8\mapsto 2\mapsto 1),(8\mapsto 8\mapsto 3\mapsto 1),(8\mapsto 8\mapsto 3\mapsto 2),(8\mapsto 8\mapsto 5\mapsto 4),(8\mapsto 8\mapsto 6\mapsto 4),(8\mapsto 8\mapsto 6\mapsto 5),(8\mapsto 8\mapsto 8\mapsto 7),(8\mapsto 8\mapsto 9\mapsto 7),(8\mapsto 8\mapsto 9\mapsto 8),(9\mapsto 7\mapsto 1\mapsto 1),(9\mapsto 7\mapsto 1\mapsto 2),(9\mapsto 7\mapsto 1\mapsto 3),(9\mapsto 7\mapsto 2\mapsto 1),(9\mapsto 7\mapsto 2\mapsto 2),(9\mapsto 7\mapsto 2\mapsto 3),(9\mapsto 7\mapsto 3\mapsto 1),(9\mapsto 7\mapsto 3\mapsto 2),(9\mapsto 7\mapsto 3\mapsto 3),(9\mapsto 7\mapsto 4\mapsto 4),(9\mapsto 7\mapsto 4\mapsto 5),(9\mapsto 7\mapsto 4\mapsto 6),(9\mapsto 7\mapsto 5\mapsto 4),(9\mapsto 7\mapsto 5\mapsto 5),(9\mapsto 7\mapsto 5\mapsto 6),(9\mapsto 7\mapsto 6\mapsto 4),(9\mapsto 7\mapsto 6\mapsto 5),(9\mapsto 7\mapsto 6\mapsto 6),(9\mapsto 7\mapsto 7\mapsto 7),(9\mapsto 7\mapsto 7\mapsto 8),(9\mapsto 7\mapsto 7\mapsto 9),(9\mapsto 7\mapsto 8\mapsto 7),(9\mapsto 7\mapsto 8\mapsto 8),(9\mapsto 7\mapsto 8\mapsto 9),(9\mapsto 7\mapsto 9\mapsto 7),(9\mapsto 7\mapsto 9\mapsto 8),(9\mapsto 7\mapsto 9\mapsto 9),(9\mapsto 8\mapsto 1\mapsto 1),(9\mapsto 8\mapsto 1\mapsto 2),(9\mapsto 8\mapsto 1\mapsto 3),(9\mapsto 8\mapsto 2\mapsto 1),(9\mapsto 8\mapsto 2\mapsto 2),(9\mapsto 8\mapsto 2\mapsto 3),(9\mapsto 8\mapsto 3\mapsto 1),(9\mapsto 8\mapsto 3\mapsto 2),(9\mapsto 8\mapsto 3\mapsto 3),(9\mapsto 8\mapsto 4\mapsto 4),(9\mapsto 8\mapsto 4\mapsto 5),(9\mapsto 8\mapsto 4\mapsto 6),(9\mapsto 8\mapsto 5\mapsto 4),(9\mapsto 8\mapsto 5\mapsto 5),(9\mapsto 8\mapsto 5\mapsto 6),(9\mapsto 8\mapsto 6\mapsto 4),(9\mapsto 8\mapsto 6\mapsto 5),(9\mapsto 8\mapsto 6\mapsto 6),(9\mapsto 8\mapsto 7\mapsto 7),(9\mapsto 8\mapsto 7\mapsto 8),(9\mapsto 8\mapsto 7\mapsto 9),(9\mapsto 8\mapsto 8\mapsto 7),(9\mapsto 8\mapsto 8\mapsto 8),(9\mapsto 8\mapsto 8\mapsto 9),(9\mapsto 8\mapsto 9\mapsto 7),(9\mapsto 8\mapsto 9\mapsto 8),(9\mapsto 8\mapsto 9\mapsto 9),(9\mapsto 9\mapsto 2\mapsto 1),(9\mapsto 9\mapsto 3\mapsto 1),(9\mapsto 9\mapsto 3\mapsto 2),(9\mapsto 9\mapsto 5\mapsto 4),(9\mapsto 9\mapsto 6\mapsto 4),(9\mapsto 9\mapsto 6\mapsto 5),(9\mapsto 9\mapsto 8\mapsto 7),(9\mapsto 9\mapsto 9\mapsto 7),(9\mapsto 9\mapsto 9\mapsto 8)\}$
* $\mathit{Diff2} = \{(1\mapsto 1\mapsto 1\mapsto 2),(1\mapsto 1\mapsto 1\mapsto 3),(1\mapsto 1\mapsto 1\mapsto 4),(1\mapsto 1\mapsto 1\mapsto 5),(1\mapsto 1\mapsto 1\mapsto 6),(1\mapsto 1\mapsto 1\mapsto 7),(1\mapsto 1\mapsto 1\mapsto 8),(1\mapsto 1\mapsto 1\mapsto 9),(1\mapsto 1\mapsto 2\mapsto 3),(1\mapsto 1\mapsto 2\mapsto 4),(1\mapsto 1\mapsto 2\mapsto 5),(1\mapsto 1\mapsto 2\mapsto 6),(1\mapsto 1\mapsto 2\mapsto 7),(1\mapsto 1\mapsto 2\mapsto 8),(1\mapsto 1\mapsto 2\mapsto 9),(1\mapsto 1\mapsto 3\mapsto 4),(1\mapsto 1\mapsto 3\mapsto 5),(1\mapsto 1\mapsto 3\mapsto 6),(1\mapsto 1\mapsto 3\mapsto 7),(1\mapsto 1\mapsto 3\mapsto 8),(1\mapsto 1\mapsto 3\mapsto 9),(1\mapsto 1\mapsto 4\mapsto 5),(1\mapsto 1\mapsto 4\mapsto 6),(1\mapsto 1\mapsto 4\mapsto 7),(1\mapsto 1\mapsto 4\mapsto 8),(1\mapsto 1\mapsto 4\mapsto 9),(1\mapsto 1\mapsto 5\mapsto 6),(1\mapsto 1\mapsto 5\mapsto 7),(1\mapsto 1\mapsto 5\mapsto 8),(1\mapsto 1\mapsto 5\mapsto 9),(1\mapsto 1\mapsto 6\mapsto 7),(1\mapsto 1\mapsto 6\mapsto 8),(1\mapsto 1\mapsto 6\mapsto 9),(1\mapsto 1\mapsto 7\mapsto 8),(1\mapsto 1\mapsto 7\mapsto 9),(1\mapsto 1\mapsto 8\mapsto 9),(2\mapsto 2\mapsto 1\mapsto 2),(2\mapsto 2\mapsto 1\mapsto 3),(2\mapsto 2\mapsto 1\mapsto 4),(2\mapsto 2\mapsto 1\mapsto 5),(2\mapsto 2\mapsto 1\mapsto 6),(2\mapsto 2\mapsto 1\mapsto 7),(2\mapsto 2\mapsto 1\mapsto 8),(2\mapsto 2\mapsto 1\mapsto 9),(2\mapsto 2\mapsto 2\mapsto 3),(2\mapsto 2\mapsto 2\mapsto 4),(2\mapsto 2\mapsto 2\mapsto 5),(2\mapsto 2\mapsto 2\mapsto 6),(2\mapsto 2\mapsto 2\mapsto 7),(2\mapsto 2\mapsto 2\mapsto 8),(2\mapsto 2\mapsto 2\mapsto 9),(2\mapsto 2\mapsto 3\mapsto 4),(2\mapsto 2\mapsto 3\mapsto 5),(2\mapsto 2\mapsto 3\mapsto 6),(2\mapsto 2\mapsto 3\mapsto 7),(2\mapsto 2\mapsto 3\mapsto 8),(2\mapsto 2\mapsto 3\mapsto 9),(2\mapsto 2\mapsto 4\mapsto 5),(2\mapsto 2\mapsto 4\mapsto 6),(2\mapsto 2\mapsto 4\mapsto 7),(2\mapsto 2\mapsto 4\mapsto 8),(2\mapsto 2\mapsto 4\mapsto 9),(2\mapsto 2\mapsto 5\mapsto 6),(2\mapsto 2\mapsto 5\mapsto 7),(2\mapsto 2\mapsto 5\mapsto 8),(2\mapsto 2\mapsto 5\mapsto 9),(2\mapsto 2\mapsto 6\mapsto 7),(2\mapsto 2\mapsto 6\mapsto 8),(2\mapsto 2\mapsto 6\mapsto 9),(2\mapsto 2\mapsto 7\mapsto 8),(2\mapsto 2\mapsto 7\mapsto 9),(2\mapsto 2\mapsto 8\mapsto 9),(3\mapsto 3\mapsto 1\mapsto 2),(3\mapsto 3\mapsto 1\mapsto 3),(3\mapsto 3\mapsto 1\mapsto 4),(3\mapsto 3\mapsto 1\mapsto 5),(3\mapsto 3\mapsto 1\mapsto 6),(3\mapsto 3\mapsto 1\mapsto 7),(3\mapsto 3\mapsto 1\mapsto 8),(3\mapsto 3\mapsto 1\mapsto 9),(3\mapsto 3\mapsto 2\mapsto 3),(3\mapsto 3\mapsto 2\mapsto 4),(3\mapsto 3\mapsto 2\mapsto 5),(3\mapsto 3\mapsto 2\mapsto 6),(3\mapsto 3\mapsto 2\mapsto 7),(3\mapsto 3\mapsto 2\mapsto 8),(3\mapsto 3\mapsto 2\mapsto 9),(3\mapsto 3\mapsto 3\mapsto 4),(3\mapsto 3\mapsto 3\mapsto 5),(3\mapsto 3\mapsto 3\mapsto 6),(3\mapsto 3\mapsto 3\mapsto 7),(3\mapsto 3\mapsto 3\mapsto 8),(3\mapsto 3\mapsto 3\mapsto 9),(3\mapsto 3\mapsto 4\mapsto 5),(3\mapsto 3\mapsto 4\mapsto 6),(3\mapsto 3\mapsto 4\mapsto 7),(3\mapsto 3\mapsto 4\mapsto 8),(3\mapsto 3\mapsto 4\mapsto 9),(3\mapsto 3\mapsto 5\mapsto 6),(3\mapsto 3\mapsto 5\mapsto 7),(3\mapsto 3\mapsto 5\mapsto 8),(3\mapsto 3\mapsto 5\mapsto 9),(3\mapsto 3\mapsto 6\mapsto 7),(3\mapsto 3\mapsto 6\mapsto 8),(3\mapsto 3\mapsto 6\mapsto 9),(3\mapsto 3\mapsto 7\mapsto 8),(3\mapsto 3\mapsto 7\mapsto 9),(3\mapsto 3\mapsto 8\mapsto 9),(4\mapsto 4\mapsto 1\mapsto 2),(4\mapsto 4\mapsto 1\mapsto 3),(4\mapsto 4\mapsto 1\mapsto 4),(4\mapsto 4\mapsto 1\mapsto 5),(4\mapsto 4\mapsto 1\mapsto 6),(4\mapsto 4\mapsto 1\mapsto 7),(4\mapsto 4\mapsto 1\mapsto 8),(4\mapsto 4\mapsto 1\mapsto 9),(4\mapsto 4\mapsto 2\mapsto 3),(4\mapsto 4\mapsto 2\mapsto 4),(4\mapsto 4\mapsto 2\mapsto 5),(4\mapsto 4\mapsto 2\mapsto 6),(4\mapsto 4\mapsto 2\mapsto 7),(4\mapsto 4\mapsto 2\mapsto 8),(4\mapsto 4\mapsto 2\mapsto 9),(4\mapsto 4\mapsto 3\mapsto 4),(4\mapsto 4\mapsto 3\mapsto 5),(4\mapsto 4\mapsto 3\mapsto 6),(4\mapsto 4\mapsto 3\mapsto 7),(4\mapsto 4\mapsto 3\mapsto 8),(4\mapsto 4\mapsto 3\mapsto 9),(4\mapsto 4\mapsto 4\mapsto 5),(4\mapsto 4\mapsto 4\mapsto 6),(4\mapsto 4\mapsto 4\mapsto 7),(4\mapsto 4\mapsto 4\mapsto 8),(4\mapsto 4\mapsto 4\mapsto 9),(4\mapsto 4\mapsto 5\mapsto 6),(4\mapsto 4\mapsto 5\mapsto 7),(4\mapsto 4\mapsto 5\mapsto 8),(4\mapsto 4\mapsto 5\mapsto 9),(4\mapsto 4\mapsto 6\mapsto 7),(4\mapsto 4\mapsto 6\mapsto 8),(4\mapsto 4\mapsto 6\mapsto 9),(4\mapsto 4\mapsto 7\mapsto 8),(4\mapsto 4\mapsto 7\mapsto 9),(4\mapsto 4\mapsto 8\mapsto 9),(5\mapsto 5\mapsto 1\mapsto 2),(5\mapsto 5\mapsto 1\mapsto 3),(5\mapsto 5\mapsto 1\mapsto 4),(5\mapsto 5\mapsto 1\mapsto 5),(5\mapsto 5\mapsto 1\mapsto 6),(5\mapsto 5\mapsto 1\mapsto 7),(5\mapsto 5\mapsto 1\mapsto 8),(5\mapsto 5\mapsto 1\mapsto 9),(5\mapsto 5\mapsto 2\mapsto 3),(5\mapsto 5\mapsto 2\mapsto 4),(5\mapsto 5\mapsto 2\mapsto 5),(5\mapsto 5\mapsto 2\mapsto 6),(5\mapsto 5\mapsto 2\mapsto 7),(5\mapsto 5\mapsto 2\mapsto 8),(5\mapsto 5\mapsto 2\mapsto 9),(5\mapsto 5\mapsto 3\mapsto 4),(5\mapsto 5\mapsto 3\mapsto 5),(5\mapsto 5\mapsto 3\mapsto 6),(5\mapsto 5\mapsto 3\mapsto 7),(5\mapsto 5\mapsto 3\mapsto 8),(5\mapsto 5\mapsto 3\mapsto 9),(5\mapsto 5\mapsto 4\mapsto 5),(5\mapsto 5\mapsto 4\mapsto 6),(5\mapsto 5\mapsto 4\mapsto 7),(5\mapsto 5\mapsto 4\mapsto 8),(5\mapsto 5\mapsto 4\mapsto 9),(5\mapsto 5\mapsto 5\mapsto 6),(5\mapsto 5\mapsto 5\mapsto 7),(5\mapsto 5\mapsto 5\mapsto 8),(5\mapsto 5\mapsto 5\mapsto 9),(5\mapsto 5\mapsto 6\mapsto 7),(5\mapsto 5\mapsto 6\mapsto 8),(5\mapsto 5\mapsto 6\mapsto 9),(5\mapsto 5\mapsto 7\mapsto 8),(5\mapsto 5\mapsto 7\mapsto 9),(5\mapsto 5\mapsto 8\mapsto 9),(6\mapsto 6\mapsto 1\mapsto 2),(6\mapsto 6\mapsto 1\mapsto 3),(6\mapsto 6\mapsto 1\mapsto 4),(6\mapsto 6\mapsto 1\mapsto 5),(6\mapsto 6\mapsto 1\mapsto 6),(6\mapsto 6\mapsto 1\mapsto 7),(6\mapsto 6\mapsto 1\mapsto 8),(6\mapsto 6\mapsto 1\mapsto 9),(6\mapsto 6\mapsto 2\mapsto 3),(6\mapsto 6\mapsto 2\mapsto 4),(6\mapsto 6\mapsto 2\mapsto 5),(6\mapsto 6\mapsto 2\mapsto 6),(6\mapsto 6\mapsto 2\mapsto 7),(6\mapsto 6\mapsto 2\mapsto 8),(6\mapsto 6\mapsto 2\mapsto 9),(6\mapsto 6\mapsto 3\mapsto 4),(6\mapsto 6\mapsto 3\mapsto 5),(6\mapsto 6\mapsto 3\mapsto 6),(6\mapsto 6\mapsto 3\mapsto 7),(6\mapsto 6\mapsto 3\mapsto 8),(6\mapsto 6\mapsto 3\mapsto 9),(6\mapsto 6\mapsto 4\mapsto 5),(6\mapsto 6\mapsto 4\mapsto 6),(6\mapsto 6\mapsto 4\mapsto 7),(6\mapsto 6\mapsto 4\mapsto 8),(6\mapsto 6\mapsto 4\mapsto 9),(6\mapsto 6\mapsto 5\mapsto 6),(6\mapsto 6\mapsto 5\mapsto 7),(6\mapsto 6\mapsto 5\mapsto 8),(6\mapsto 6\mapsto 5\mapsto 9),(6\mapsto 6\mapsto 6\mapsto 7),(6\mapsto 6\mapsto 6\mapsto 8),(6\mapsto 6\mapsto 6\mapsto 9),(6\mapsto 6\mapsto 7\mapsto 8),(6\mapsto 6\mapsto 7\mapsto 9),(6\mapsto 6\mapsto 8\mapsto 9),(7\mapsto 7\mapsto 1\mapsto 2),(7\mapsto 7\mapsto 1\mapsto 3),(7\mapsto 7\mapsto 1\mapsto 4),(7\mapsto 7\mapsto 1\mapsto 5),(7\mapsto 7\mapsto 1\mapsto 6),(7\mapsto 7\mapsto 1\mapsto 7),(7\mapsto 7\mapsto 1\mapsto 8),(7\mapsto 7\mapsto 1\mapsto 9),(7\mapsto 7\mapsto 2\mapsto 3),(7\mapsto 7\mapsto 2\mapsto 4),(7\mapsto 7\mapsto 2\mapsto 5),(7\mapsto 7\mapsto 2\mapsto 6),(7\mapsto 7\mapsto 2\mapsto 7),(7\mapsto 7\mapsto 2\mapsto 8),(7\mapsto 7\mapsto 2\mapsto 9),(7\mapsto 7\mapsto 3\mapsto 4),(7\mapsto 7\mapsto 3\mapsto 5),(7\mapsto 7\mapsto 3\mapsto 6),(7\mapsto 7\mapsto 3\mapsto 7),(7\mapsto 7\mapsto 3\mapsto 8),(7\mapsto 7\mapsto 3\mapsto 9),(7\mapsto 7\mapsto 4\mapsto 5),(7\mapsto 7\mapsto 4\mapsto 6),(7\mapsto 7\mapsto 4\mapsto 7),(7\mapsto 7\mapsto 4\mapsto 8),(7\mapsto 7\mapsto 4\mapsto 9),(7\mapsto 7\mapsto 5\mapsto 6),(7\mapsto 7\mapsto 5\mapsto 7),(7\mapsto 7\mapsto 5\mapsto 8),(7\mapsto 7\mapsto 5\mapsto 9),(7\mapsto 7\mapsto 6\mapsto 7),(7\mapsto 7\mapsto 6\mapsto 8),(7\mapsto 7\mapsto 6\mapsto 9),(7\mapsto 7\mapsto 7\mapsto 8),(7\mapsto 7\mapsto 7\mapsto 9),(7\mapsto 7\mapsto 8\mapsto 9),(8\mapsto 8\mapsto 1\mapsto 2),(8\mapsto 8\mapsto 1\mapsto 3),(8\mapsto 8\mapsto 1\mapsto 4),(8\mapsto 8\mapsto 1\mapsto 5),(8\mapsto 8\mapsto 1\mapsto 6),(8\mapsto 8\mapsto 1\mapsto 7),(8\mapsto 8\mapsto 1\mapsto 8),(8\mapsto 8\mapsto 1\mapsto 9),(8\mapsto 8\mapsto 2\mapsto 3),(8\mapsto 8\mapsto 2\mapsto 4),(8\mapsto 8\mapsto 2\mapsto 5),(8\mapsto 8\mapsto 2\mapsto 6),(8\mapsto 8\mapsto 2\mapsto 7),(8\mapsto 8\mapsto 2\mapsto 8),(8\mapsto 8\mapsto 2\mapsto 9),(8\mapsto 8\mapsto 3\mapsto 4),(8\mapsto 8\mapsto 3\mapsto 5),(8\mapsto 8\mapsto 3\mapsto 6),(8\mapsto 8\mapsto 3\mapsto 7),(8\mapsto 8\mapsto 3\mapsto 8),(8\mapsto 8\mapsto 3\mapsto 9),(8\mapsto 8\mapsto 4\mapsto 5),(8\mapsto 8\mapsto 4\mapsto 6),(8\mapsto 8\mapsto 4\mapsto 7),(8\mapsto 8\mapsto 4\mapsto 8),(8\mapsto 8\mapsto 4\mapsto 9),(8\mapsto 8\mapsto 5\mapsto 6),(8\mapsto 8\mapsto 5\mapsto 7),(8\mapsto 8\mapsto 5\mapsto 8),(8\mapsto 8\mapsto 5\mapsto 9),(8\mapsto 8\mapsto 6\mapsto 7),(8\mapsto 8\mapsto 6\mapsto 8),(8\mapsto 8\mapsto 6\mapsto 9),(8\mapsto 8\mapsto 7\mapsto 8),(8\mapsto 8\mapsto 7\mapsto 9),(8\mapsto 8\mapsto 8\mapsto 9),(9\mapsto 9\mapsto 1\mapsto 2),(9\mapsto 9\mapsto 1\mapsto 3),(9\mapsto 9\mapsto 1\mapsto 4),(9\mapsto 9\mapsto 1\mapsto 5),(9\mapsto 9\mapsto 1\mapsto 6),(9\mapsto 9\mapsto 1\mapsto 7),(9\mapsto 9\mapsto 1\mapsto 8),(9\mapsto 9\mapsto 1\mapsto 9),(9\mapsto 9\mapsto 2\mapsto 3),(9\mapsto 9\mapsto 2\mapsto 4),(9\mapsto 9\mapsto 2\mapsto 5),(9\mapsto 9\mapsto 2\mapsto 6),(9\mapsto 9\mapsto 2\mapsto 7),(9\mapsto 9\mapsto 2\mapsto 8),(9\mapsto 9\mapsto 2\mapsto 9),(9\mapsto 9\mapsto 3\mapsto 4),(9\mapsto 9\mapsto 3\mapsto 5),(9\mapsto 9\mapsto 3\mapsto 6),(9\mapsto 9\mapsto 3\mapsto 7),(9\mapsto 9\mapsto 3\mapsto 8),(9\mapsto 9\mapsto 3\mapsto 9),(9\mapsto 9\mapsto 4\mapsto 5),(9\mapsto 9\mapsto 4\mapsto 6),(9\mapsto 9\mapsto 4\mapsto 7),(9\mapsto 9\mapsto 4\mapsto 8),(9\mapsto 9\mapsto 4\mapsto 9),(9\mapsto 9\mapsto 5\mapsto 6),(9\mapsto 9\mapsto 5\mapsto 7),(9\mapsto 9\mapsto 5\mapsto 8),(9\mapsto 9\mapsto 5\mapsto 9),(9\mapsto 9\mapsto 6\mapsto 7),(9\mapsto 9\mapsto 6\mapsto 8),(9\mapsto 9\mapsto 6\mapsto 9),(9\mapsto 9\mapsto 7\mapsto 8),(9\mapsto 9\mapsto 7\mapsto 9),(9\mapsto 9\mapsto 8\mapsto 9)\}$
* $\mathit{Board} = \{(1\mapsto\{(1\mapsto 7),(2\mapsto 8),(3\mapsto 1),(4\mapsto 1),(5\mapsto 1),(6\mapsto 1),(7\mapsto 1),(8\mapsto 1),(9\mapsto 1)\}),(2\mapsto\{(1\mapsto 9),(2\mapsto 1),(3\mapsto 1),(4\mapsto 1),(5\mapsto 1),(6\mapsto 1),(7\mapsto 1),(8\mapsto 1),(9\mapsto 1)\}),(3\mapsto\{(1\mapsto 1),(2\mapsto 1),(3\mapsto 1),(4\mapsto 1),(5\mapsto 1),(6\mapsto 1),(7\mapsto 1),(8\mapsto 1),(9\mapsto 1)\}),(4\mapsto\{(1\mapsto 1),(2\mapsto 1),(3\mapsto 1),(4\mapsto 1),(5\mapsto 1),(6\mapsto 1),(7\mapsto 1),(8\mapsto 1),(9\mapsto 1)\}),(5\mapsto\{(1\mapsto 1),(2\mapsto 1),(3\mapsto 1),(4\mapsto 1),(5\mapsto 1),(6\mapsto 1),(7\mapsto 1),(8\mapsto 1),(9\mapsto 1)\}),(6\mapsto\{(1\mapsto 1),(2\mapsto 1),(3\mapsto 1),(4\mapsto 1),(5\mapsto 1),(6\mapsto 1),(7\mapsto 1),(8\mapsto 1),(9\mapsto 1)\}),(7\mapsto\{(1\mapsto 1),(2\mapsto 1),(3\mapsto 1),(4\mapsto 1),(5\mapsto 1),(6\mapsto 1),(7\mapsto 1),(8\mapsto 1),(9\mapsto 1)\}),(8\mapsto\{(1\mapsto 1),(2\mapsto 1),(3\mapsto 1),(4\mapsto 1),(5\mapsto 1),(6\mapsto 1),(7\mapsto 1),(8\mapsto 1),(9\mapsto 1)\}),(9\mapsto\{(1\mapsto 1),(2\mapsto 1),(3\mapsto 1),(4\mapsto 1),(5\mapsto 1),(6\mapsto 1),(7\mapsto 1),(8\mapsto 1),(9\mapsto 1)\})\}$
* $\mathit{DOM} = \{1,2,3,4,5,6,7,8,9\}$
* $\mathit{Diff1} = \{(1\mapsto 2\mapsto 1\mapsto 1),(1\mapsto 2\mapsto 2\mapsto 2),(1\mapsto 2\mapsto 3\mapsto 3),(1\mapsto 2\mapsto 4\mapsto 4),(1\mapsto 2\mapsto 5\mapsto 5),(1\mapsto 2\mapsto 6\mapsto 6),(1\mapsto 2\mapsto 7\mapsto 7),(1\mapsto 2\mapsto 8\mapsto 8),(1\mapsto 2\mapsto 9\mapsto 9),(1\mapsto 3\mapsto 1\mapsto 1),(1\mapsto 3\mapsto 2\mapsto 2),(1\mapsto 3\mapsto 3\mapsto 3),(1\mapsto 3\mapsto 4\mapsto 4),(1\mapsto 3\mapsto 5\mapsto 5),(1\mapsto 3\mapsto 6\mapsto 6),(1\mapsto 3\mapsto 7\mapsto 7),(1\mapsto 3\mapsto 8\mapsto 8),(1\mapsto 3\mapsto 9\mapsto 9),(1\mapsto 4\mapsto 1\mapsto 1),(1\mapsto 4\mapsto 2\mapsto 2),(1\mapsto 4\mapsto 3\mapsto 3),(1\mapsto 4\mapsto 4\mapsto 4),(1\mapsto 4\mapsto 5\mapsto 5),(1\mapsto 4\mapsto 6\mapsto 6),(1\mapsto 4\mapsto 7\mapsto 7),(1\mapsto 4\mapsto 8\mapsto 8),(1\mapsto 4\mapsto 9\mapsto 9),(1\mapsto 5\mapsto 1\mapsto 1),(1\mapsto 5\mapsto 2\mapsto 2),(1\mapsto 5\mapsto 3\mapsto 3),(1\mapsto 5\mapsto 4\mapsto 4),(1\mapsto 5\mapsto 5\mapsto 5),(1\mapsto 5\mapsto 6\mapsto 6),(1\mapsto 5\mapsto 7\mapsto 7),(1\mapsto 5\mapsto 8\mapsto 8),(1\mapsto 5\mapsto 9\mapsto 9),(1\mapsto 6\mapsto 1\mapsto 1),(1\mapsto 6\mapsto 2\mapsto 2),(1\mapsto 6\mapsto 3\mapsto 3),(1\mapsto 6\mapsto 4\mapsto 4),(1\mapsto 6\mapsto 5\mapsto 5),(1\mapsto 6\mapsto 6\mapsto 6),(1\mapsto 6\mapsto 7\mapsto 7),(1\mapsto 6\mapsto 8\mapsto 8),(1\mapsto 6\mapsto 9\mapsto 9),(1\mapsto 7\mapsto 1\mapsto 1),(1\mapsto 7\mapsto 2\mapsto 2),(1\mapsto 7\mapsto 3\mapsto 3),(1\mapsto 7\mapsto 4\mapsto 4),(1\mapsto 7\mapsto 5\mapsto 5),(1\mapsto 7\mapsto 6\mapsto 6),(1\mapsto 7\mapsto 7\mapsto 7),(1\mapsto 7\mapsto 8\mapsto 8),(1\mapsto 7\mapsto 9\mapsto 9),(1\mapsto 8\mapsto 1\mapsto 1),(1\mapsto 8\mapsto 2\mapsto 2),(1\mapsto 8\mapsto 3\mapsto 3),(1\mapsto 8\mapsto 4\mapsto 4),(1\mapsto 8\mapsto 5\mapsto 5),(1\mapsto 8\mapsto 6\mapsto 6),(1\mapsto 8\mapsto 7\mapsto 7),(1\mapsto 8\mapsto 8\mapsto 8),(1\mapsto 8\mapsto 9\mapsto 9),(1\mapsto 9\mapsto 1\mapsto 1),(1\mapsto 9\mapsto 2\mapsto 2),(1\mapsto 9\mapsto 3\mapsto 3),(1\mapsto 9\mapsto 4\mapsto 4),(1\mapsto 9\mapsto 5\mapsto 5),(1\mapsto 9\mapsto 6\mapsto 6),(1\mapsto 9\mapsto 7\mapsto 7),(1\mapsto 9\mapsto 8\mapsto 8),(1\mapsto 9\mapsto 9\mapsto 9),(2\mapsto 3\mapsto 1\mapsto 1),(2\mapsto 3\mapsto 2\mapsto 2),(2\mapsto 3\mapsto 3\mapsto 3),(2\mapsto 3\mapsto 4\mapsto 4),(2\mapsto 3\mapsto 5\mapsto 5),(2\mapsto 3\mapsto 6\mapsto 6),(2\mapsto 3\mapsto 7\mapsto 7),(2\mapsto 3\mapsto 8\mapsto 8),(2\mapsto 3\mapsto 9\mapsto 9),(2\mapsto 4\mapsto 1\mapsto 1),(2\mapsto 4\mapsto 2\mapsto 2),(2\mapsto 4\mapsto 3\mapsto 3),(2\mapsto 4\mapsto 4\mapsto 4),(2\mapsto 4\mapsto 5\mapsto 5),(2\mapsto 4\mapsto 6\mapsto 6),(2\mapsto 4\mapsto 7\mapsto 7),(2\mapsto 4\mapsto 8\mapsto 8),(2\mapsto 4\mapsto 9\mapsto 9),(2\mapsto 5\mapsto 1\mapsto 1),(2\mapsto 5\mapsto 2\mapsto 2),(2\mapsto 5\mapsto 3\mapsto 3),(2\mapsto 5\mapsto 4\mapsto 4),(2\mapsto 5\mapsto 5\mapsto 5),(2\mapsto 5\mapsto 6\mapsto 6),(2\mapsto 5\mapsto 7\mapsto 7),(2\mapsto 5\mapsto 8\mapsto 8),(2\mapsto 5\mapsto 9\mapsto 9),(2\mapsto 6\mapsto 1\mapsto 1),(2\mapsto 6\mapsto 2\mapsto 2),(2\mapsto 6\mapsto 3\mapsto 3),(2\mapsto 6\mapsto 4\mapsto 4),(2\mapsto 6\mapsto 5\mapsto 5),(2\mapsto 6\mapsto 6\mapsto 6),(2\mapsto 6\mapsto 7\mapsto 7),(2\mapsto 6\mapsto 8\mapsto 8),(2\mapsto 6\mapsto 9\mapsto 9),(2\mapsto 7\mapsto 1\mapsto 1),(2\mapsto 7\mapsto 2\mapsto 2),(2\mapsto 7\mapsto 3\mapsto 3),(2\mapsto 7\mapsto 4\mapsto 4),(2\mapsto 7\mapsto 5\mapsto 5),(2\mapsto 7\mapsto 6\mapsto 6),(2\mapsto 7\mapsto 7\mapsto 7),(2\mapsto 7\mapsto 8\mapsto 8),(2\mapsto 7\mapsto 9\mapsto 9),(2\mapsto 8\mapsto 1\mapsto 1),(2\mapsto 8\mapsto 2\mapsto 2),(2\mapsto 8\mapsto 3\mapsto 3),(2\mapsto 8\mapsto 4\mapsto 4),(2\mapsto 8\mapsto 5\mapsto 5),(2\mapsto 8\mapsto 6\mapsto 6),(2\mapsto 8\mapsto 7\mapsto 7),(2\mapsto 8\mapsto 8\mapsto 8),(2\mapsto 8\mapsto 9\mapsto 9),(2\mapsto 9\mapsto 1\mapsto 1),(2\mapsto 9\mapsto 2\mapsto 2),(2\mapsto 9\mapsto 3\mapsto 3),(2\mapsto 9\mapsto 4\mapsto 4),(2\mapsto 9\mapsto 5\mapsto 5),(2\mapsto 9\mapsto 6\mapsto 6),(2\mapsto 9\mapsto 7\mapsto 7),(2\mapsto 9\mapsto 8\mapsto 8),(2\mapsto 9\mapsto 9\mapsto 9),(3\mapsto 4\mapsto 1\mapsto 1),(3\mapsto 4\mapsto 2\mapsto 2),(3\mapsto 4\mapsto 3\mapsto 3),(3\mapsto 4\mapsto 4\mapsto 4),(3\mapsto 4\mapsto 5\mapsto 5),(3\mapsto 4\mapsto 6\mapsto 6),(3\mapsto 4\mapsto 7\mapsto 7),(3\mapsto 4\mapsto 8\mapsto 8),(3\mapsto 4\mapsto 9\mapsto 9),(3\mapsto 5\mapsto 1\mapsto 1),(3\mapsto 5\mapsto 2\mapsto 2),(3\mapsto 5\mapsto 3\mapsto 3),(3\mapsto 5\mapsto 4\mapsto 4),(3\mapsto 5\mapsto 5\mapsto 5),(3\mapsto 5\mapsto 6\mapsto 6),(3\mapsto 5\mapsto 7\mapsto 7),(3\mapsto 5\mapsto 8\mapsto 8),(3\mapsto 5\mapsto 9\mapsto 9),(3\mapsto 6\mapsto 1\mapsto 1),(3\mapsto 6\mapsto 2\mapsto 2),(3\mapsto 6\mapsto 3\mapsto 3),(3\mapsto 6\mapsto 4\mapsto 4),(3\mapsto 6\mapsto 5\mapsto 5),(3\mapsto 6\mapsto 6\mapsto 6),(3\mapsto 6\mapsto 7\mapsto 7),(3\mapsto 6\mapsto 8\mapsto 8),(3\mapsto 6\mapsto 9\mapsto 9),(3\mapsto 7\mapsto 1\mapsto 1),(3\mapsto 7\mapsto 2\mapsto 2),(3\mapsto 7\mapsto 3\mapsto 3),(3\mapsto 7\mapsto 4\mapsto 4),(3\mapsto 7\mapsto 5\mapsto 5),(3\mapsto 7\mapsto 6\mapsto 6),(3\mapsto 7\mapsto 7\mapsto 7),(3\mapsto 7\mapsto 8\mapsto 8),(3\mapsto 7\mapsto 9\mapsto 9),(3\mapsto 8\mapsto 1\mapsto 1),(3\mapsto 8\mapsto 2\mapsto 2),(3\mapsto 8\mapsto 3\mapsto 3),(3\mapsto 8\mapsto 4\mapsto 4),(3\mapsto 8\mapsto 5\mapsto 5),(3\mapsto 8\mapsto 6\mapsto 6),(3\mapsto 8\mapsto 7\mapsto 7),(3\mapsto 8\mapsto 8\mapsto 8),(3\mapsto 8\mapsto 9\mapsto 9),(3\mapsto 9\mapsto 1\mapsto 1),(3\mapsto 9\mapsto 2\mapsto 2),(3\mapsto 9\mapsto 3\mapsto 3),(3\mapsto 9\mapsto 4\mapsto 4),(3\mapsto 9\mapsto 5\mapsto 5),(3\mapsto 9\mapsto 6\mapsto 6),(3\mapsto 9\mapsto 7\mapsto 7),(3\mapsto 9\mapsto 8\mapsto 8),(3\mapsto 9\mapsto 9\mapsto 9),(4\mapsto 5\mapsto 1\mapsto 1),(4\mapsto 5\mapsto 2\mapsto 2),(4\mapsto 5\mapsto 3\mapsto 3),(4\mapsto 5\mapsto 4\mapsto 4),(4\mapsto 5\mapsto 5\mapsto 5),(4\mapsto 5\mapsto 6\mapsto 6),(4\mapsto 5\mapsto 7\mapsto 7),(4\mapsto 5\mapsto 8\mapsto 8),(4\mapsto 5\mapsto 9\mapsto 9),(4\mapsto 6\mapsto 1\mapsto 1),(4\mapsto 6\mapsto 2\mapsto 2),(4\mapsto 6\mapsto 3\mapsto 3),(4\mapsto 6\mapsto 4\mapsto 4),(4\mapsto 6\mapsto 5\mapsto 5),(4\mapsto 6\mapsto 6\mapsto 6),(4\mapsto 6\mapsto 7\mapsto 7),(4\mapsto 6\mapsto 8\mapsto 8),(4\mapsto 6\mapsto 9\mapsto 9),(4\mapsto 7\mapsto 1\mapsto 1),(4\mapsto 7\mapsto 2\mapsto 2),(4\mapsto 7\mapsto 3\mapsto 3),(4\mapsto 7\mapsto 4\mapsto 4),(4\mapsto 7\mapsto 5\mapsto 5),(4\mapsto 7\mapsto 6\mapsto 6),(4\mapsto 7\mapsto 7\mapsto 7),(4\mapsto 7\mapsto 8\mapsto 8),(4\mapsto 7\mapsto 9\mapsto 9),(4\mapsto 8\mapsto 1\mapsto 1),(4\mapsto 8\mapsto 2\mapsto 2),(4\mapsto 8\mapsto 3\mapsto 3),(4\mapsto 8\mapsto 4\mapsto 4),(4\mapsto 8\mapsto 5\mapsto 5),(4\mapsto 8\mapsto 6\mapsto 6),(4\mapsto 8\mapsto 7\mapsto 7),(4\mapsto 8\mapsto 8\mapsto 8),(4\mapsto 8\mapsto 9\mapsto 9),(4\mapsto 9\mapsto 1\mapsto 1),(4\mapsto 9\mapsto 2\mapsto 2),(4\mapsto 9\mapsto 3\mapsto 3),(4\mapsto 9\mapsto 4\mapsto 4),(4\mapsto 9\mapsto 5\mapsto 5),(4\mapsto 9\mapsto 6\mapsto 6),(4\mapsto 9\mapsto 7\mapsto 7),(4\mapsto 9\mapsto 8\mapsto 8),(4\mapsto 9\mapsto 9\mapsto 9),(5\mapsto 6\mapsto 1\mapsto 1),(5\mapsto 6\mapsto 2\mapsto 2),(5\mapsto 6\mapsto 3\mapsto 3),(5\mapsto 6\mapsto 4\mapsto 4),(5\mapsto 6\mapsto 5\mapsto 5),(5\mapsto 6\mapsto 6\mapsto 6),(5\mapsto 6\mapsto 7\mapsto 7),(5\mapsto 6\mapsto 8\mapsto 8),(5\mapsto 6\mapsto 9\mapsto 9),(5\mapsto 7\mapsto 1\mapsto 1),(5\mapsto 7\mapsto 2\mapsto 2),(5\mapsto 7\mapsto 3\mapsto 3),(5\mapsto 7\mapsto 4\mapsto 4),(5\mapsto 7\mapsto 5\mapsto 5),(5\mapsto 7\mapsto 6\mapsto 6),(5\mapsto 7\mapsto 7\mapsto 7),(5\mapsto 7\mapsto 8\mapsto 8),(5\mapsto 7\mapsto 9\mapsto 9),(5\mapsto 8\mapsto 1\mapsto 1),(5\mapsto 8\mapsto 2\mapsto 2),(5\mapsto 8\mapsto 3\mapsto 3),(5\mapsto 8\mapsto 4\mapsto 4),(5\mapsto 8\mapsto 5\mapsto 5),(5\mapsto 8\mapsto 6\mapsto 6),(5\mapsto 8\mapsto 7\mapsto 7),(5\mapsto 8\mapsto 8\mapsto 8),(5\mapsto 8\mapsto 9\mapsto 9),(5\mapsto 9\mapsto 1\mapsto 1),(5\mapsto 9\mapsto 2\mapsto 2),(5\mapsto 9\mapsto 3\mapsto 3),(5\mapsto 9\mapsto 4\mapsto 4),(5\mapsto 9\mapsto 5\mapsto 5),(5\mapsto 9\mapsto 6\mapsto 6),(5\mapsto 9\mapsto 7\mapsto 7),(5\mapsto 9\mapsto 8\mapsto 8),(5\mapsto 9\mapsto 9\mapsto 9),(6\mapsto 7\mapsto 1\mapsto 1),(6\mapsto 7\mapsto 2\mapsto 2),(6\mapsto 7\mapsto 3\mapsto 3),(6\mapsto 7\mapsto 4\mapsto 4),(6\mapsto 7\mapsto 5\mapsto 5),(6\mapsto 7\mapsto 6\mapsto 6),(6\mapsto 7\mapsto 7\mapsto 7),(6\mapsto 7\mapsto 8\mapsto 8),(6\mapsto 7\mapsto 9\mapsto 9),(6\mapsto 8\mapsto 1\mapsto 1),(6\mapsto 8\mapsto 2\mapsto 2),(6\mapsto 8\mapsto 3\mapsto 3),(6\mapsto 8\mapsto 4\mapsto 4),(6\mapsto 8\mapsto 5\mapsto 5),(6\mapsto 8\mapsto 6\mapsto 6),(6\mapsto 8\mapsto 7\mapsto 7),(6\mapsto 8\mapsto 8\mapsto 8),(6\mapsto 8\mapsto 9\mapsto 9),(6\mapsto 9\mapsto 1\mapsto 1),(6\mapsto 9\mapsto 2\mapsto 2),(6\mapsto 9\mapsto 3\mapsto 3),(6\mapsto 9\mapsto 4\mapsto 4),(6\mapsto 9\mapsto 5\mapsto 5),(6\mapsto 9\mapsto 6\mapsto 6),(6\mapsto 9\mapsto 7\mapsto 7),(6\mapsto 9\mapsto 8\mapsto 8),(6\mapsto 9\mapsto 9\mapsto 9),(7\mapsto 8\mapsto 1\mapsto 1),(7\mapsto 8\mapsto 2\mapsto 2),(7\mapsto 8\mapsto 3\mapsto 3),(7\mapsto 8\mapsto 4\mapsto 4),(7\mapsto 8\mapsto 5\mapsto 5),(7\mapsto 8\mapsto 6\mapsto 6),(7\mapsto 8\mapsto 7\mapsto 7),(7\mapsto 8\mapsto 8\mapsto 8),(7\mapsto 8\mapsto 9\mapsto 9),(7\mapsto 9\mapsto 1\mapsto 1),(7\mapsto 9\mapsto 2\mapsto 2),(7\mapsto 9\mapsto 3\mapsto 3),(7\mapsto 9\mapsto 4\mapsto 4),(7\mapsto 9\mapsto 5\mapsto 5),(7\mapsto 9\mapsto 6\mapsto 6),(7\mapsto 9\mapsto 7\mapsto 7),(7\mapsto 9\mapsto 8\mapsto 8),(7\mapsto 9\mapsto 9\mapsto 9),(8\mapsto 9\mapsto 1\mapsto 1),(8\mapsto 9\mapsto 2\mapsto 2),(8\mapsto 9\mapsto 3\mapsto 3),(8\mapsto 9\mapsto 4\mapsto 4),(8\mapsto 9\mapsto 5\mapsto 5),(8\mapsto 9\mapsto 6\mapsto 6),(8\mapsto 9\mapsto 7\mapsto 7),(8\mapsto 9\mapsto 8\mapsto 8),(8\mapsto 9\mapsto 9\mapsto 9)\}$
* $\mathit{Diff} = \emptyset$
* $\mathit{SUBSQ} = \{\{1,2,3\},\{4,5,6\},\{7,8,9\}\}$
TRUE
Solution:
P = {(1↦1↦7),(1↦2↦8),(1↦3↦1),(2↦1↦9)}
Diff3 = {(1↦1↦2↦1),(1↦1↦3↦1),(1↦1↦3↦2),(1↦1↦5↦4),(1↦1↦6↦4),(1↦1↦6↦5),(1↦1↦8↦7),(1↦1↦9↦7),(1↦1↦9↦8),(2↦1↦1↦1),(2↦1↦1↦2),(2↦1↦1↦3),(2↦1↦2↦1),(2↦1↦2↦2),(2↦1↦2↦3),(2↦1↦3↦1),(2↦1↦3↦2),(2↦1↦3↦3),(2↦1↦4↦4),(2↦1↦4↦5),(2↦1↦4↦6),(2↦1↦5↦4),(2↦1↦5↦5),(2↦1↦5↦6),(2↦1↦6↦4),(2↦1↦6↦5),(2↦1↦6↦6),(2↦1↦7↦7),(2↦1↦7↦8),(2↦1↦7↦9),(2↦1↦8↦7),(2↦1↦8↦8),(2↦1↦8↦9),(2↦1↦9↦7),(2↦1↦9↦8),(2↦1↦9↦9),(2↦2↦2↦1),(2↦2↦3↦1),(2↦2↦3↦2),(2↦2↦5↦4),(2↦2↦6↦4),(2↦2↦6↦5),(2↦2↦8↦7),(2↦2↦9↦7),(2↦2↦9↦8),(3↦1↦1↦1),(3↦1↦1↦2),(3↦1↦1↦3),(3↦1↦2↦1),(3↦1↦2↦2),(3↦1↦2↦3),(3↦1↦3↦1),(3↦1↦3↦2),(3↦1↦3↦3),(3↦1↦4↦4),(3↦1↦4↦5),(3↦1↦4↦6),(3↦1↦5↦4),(3↦1↦5↦5),(3↦1↦5↦6),(3↦1↦6↦4),(3↦1↦6↦5),(3↦1↦6↦6),(3↦1↦7↦7),(3↦1↦7↦8),(3↦1↦7↦9),(3↦1↦8↦7),(3↦1↦8↦8),(3↦1↦8↦9),(3↦1↦9↦7),(3↦1↦9↦8),(3↦1↦9↦9),(3↦2↦1↦1),(3↦2↦1↦2),(3↦2↦1↦3),(3↦2↦2↦1),(3↦2↦2↦2),(3↦2↦2↦3),(3↦2↦3↦1),(3↦2↦3↦2),(3↦2↦3↦3),(3↦2↦4↦4),(3↦2↦4↦5),(3↦2↦4↦6),(3↦2↦5↦4),(3↦2↦5↦5),(3↦2↦5↦6),(3↦2↦6↦4),(3↦2↦6↦5),(3↦2↦6↦6),(3↦2↦7↦7),(3↦2↦7↦8),(3↦2↦7↦9),(3↦2↦8↦7),(3↦2↦8↦8),(3↦2↦8↦9),(3↦2↦9↦7),(3↦2↦9↦8),(3↦2↦9↦9),(3↦3↦2↦1),(3↦3↦3↦1),(3↦3↦3↦2),(3↦3↦5↦4),(3↦3↦6↦4),(3↦3↦6↦5),(3↦3↦8↦7),(3↦3↦9↦7),(3↦3↦9↦8),(4↦4↦2↦1),(4↦4↦3↦1),(4↦4↦3↦2),(4↦4↦5↦4),(4↦4↦6↦4),(4↦4↦6↦5),(4↦4↦8↦7),(4↦4↦9↦7),(4↦4↦9↦8),(5↦4↦1↦1),(5↦4↦1↦2),(5↦4↦1↦3),(5↦4↦2↦1),(5↦4↦2↦2),(5↦4↦2↦3),(5↦4↦3↦1),(5↦4↦3↦2),(5↦4↦3↦3),(5↦4↦4↦4),(5↦4↦4↦5),(5↦4↦4↦6),(5↦4↦5↦4),(5↦4↦5↦5),(5↦4↦5↦6),(5↦4↦6↦4),(5↦4↦6↦5),(5↦4↦6↦6),(5↦4↦7↦7),(5↦4↦7↦8),(5↦4↦7↦9),(5↦4↦8↦7),(5↦4↦8↦8),(5↦4↦8↦9),(5↦4↦9↦7),(5↦4↦9↦8),(5↦4↦9↦9),(5↦5↦2↦1),(5↦5↦3↦1),(5↦5↦3↦2),(5↦5↦5↦4),(5↦5↦6↦4),(5↦5↦6↦5),(5↦5↦8↦7),(5↦5↦9↦7),(5↦5↦9↦8),(6↦4↦1↦1),(6↦4↦1↦2),(6↦4↦1↦3),(6↦4↦2↦1),(6↦4↦2↦2),(6↦4↦2↦3),(6↦4↦3↦1),(6↦4↦3↦2),(6↦4↦3↦3),(6↦4↦4↦4),(6↦4↦4↦5),(6↦4↦4↦6),(6↦4↦5↦4),(6↦4↦5↦5),(6↦4↦5↦6),(6↦4↦6↦4),(6↦4↦6↦5),(6↦4↦6↦6),(6↦4↦7↦7),(6↦4↦7↦8),(6↦4↦7↦9),(6↦4↦8↦7),(6↦4↦8↦8),(6↦4↦8↦9),(6↦4↦9↦7),(6↦4↦9↦8),(6↦4↦9↦9),(6↦5↦1↦1),(6↦5↦1↦2),(6↦5↦1↦3),(6↦5↦2↦1),(6↦5↦2↦2),(6↦5↦2↦3),(6↦5↦3↦1),(6↦5↦3↦2),(6↦5↦3↦3),(6↦5↦4↦4),(6↦5↦4↦5),(6↦5↦4↦6),(6↦5↦5↦4),(6↦5↦5↦5),(6↦5↦5↦6),(6↦5↦6↦4),(6↦5↦6↦5),(6↦5↦6↦6),(6↦5↦7↦7),(6↦5↦7↦8),(6↦5↦7↦9),(6↦5↦8↦7),(6↦5↦8↦8),(6↦5↦8↦9),(6↦5↦9↦7),(6↦5↦9↦8),(6↦5↦9↦9),(6↦6↦2↦1),(6↦6↦3↦1),(6↦6↦3↦2),(6↦6↦5↦4),(6↦6↦6↦4),(6↦6↦6↦5),(6↦6↦8↦7),(6↦6↦9↦7),(6↦6↦9↦8),(7↦7↦2↦1),(7↦7↦3↦1),(7↦7↦3↦2),(7↦7↦5↦4),(7↦7↦6↦4),(7↦7↦6↦5),(7↦7↦8↦7),(7↦7↦9↦7),(7↦7↦9↦8),(8↦7↦1↦1),(8↦7↦1↦2),(8↦7↦1↦3),(8↦7↦2↦1),(8↦7↦2↦2),(8↦7↦2↦3),(8↦7↦3↦1),(8↦7↦3↦2),(8↦7↦3↦3),(8↦7↦4↦4),(8↦7↦4↦5),(8↦7↦4↦6),(8↦7↦5↦4),(8↦7↦5↦5),(8↦7↦5↦6),(8↦7↦6↦4),(8↦7↦6↦5),(8↦7↦6↦6),(8↦7↦7↦7),(8↦7↦7↦8),(8↦7↦7↦9),(8↦7↦8↦7),(8↦7↦8↦8),(8↦7↦8↦9),(8↦7↦9↦7),(8↦7↦9↦8),(8↦7↦9↦9),(8↦8↦2↦1),(8↦8↦3↦1),(8↦8↦3↦2),(8↦8↦5↦4),(8↦8↦6↦4),(8↦8↦6↦5),(8↦8↦8↦7),(8↦8↦9↦7),(8↦8↦9↦8),(9↦7↦1↦1),(9↦7↦1↦2),(9↦7↦1↦3),(9↦7↦2↦1),(9↦7↦2↦2),(9↦7↦2↦3),(9↦7↦3↦1),(9↦7↦3↦2),(9↦7↦3↦3),(9↦7↦4↦4),(9↦7↦4↦5),(9↦7↦4↦6),(9↦7↦5↦4),(9↦7↦5↦5),(9↦7↦5↦6),(9↦7↦6↦4),(9↦7↦6↦5),(9↦7↦6↦6),(9↦7↦7↦7),(9↦7↦7↦8),(9↦7↦7↦9),(9↦7↦8↦7),(9↦7↦8↦8),(9↦7↦8↦9),(9↦7↦9↦7),(9↦7↦9↦8),(9↦7↦9↦9),(9↦8↦1↦1),(9↦8↦1↦2),(9↦8↦1↦3),(9↦8↦2↦1),(9↦8↦2↦2),(9↦8↦2↦3),(9↦8↦3↦1),(9↦8↦3↦2),(9↦8↦3↦3),(9↦8↦4↦4),(9↦8↦4↦5),(9↦8↦4↦6),(9↦8↦5↦4),(9↦8↦5↦5),(9↦8↦5↦6),(9↦8↦6↦4),(9↦8↦6↦5),(9↦8↦6↦6),(9↦8↦7↦7),(9↦8↦7↦8),(9↦8↦7↦9),(9↦8↦8↦7),(9↦8↦8↦8),(9↦8↦8↦9),(9↦8↦9↦7),(9↦8↦9↦8),(9↦8↦9↦9),(9↦9↦2↦1),(9↦9↦3↦1),(9↦9↦3↦2),(9↦9↦5↦4),(9↦9↦6↦4),(9↦9↦6↦5),(9↦9↦8↦7),(9↦9↦9↦7),(9↦9↦9↦8)}
Diff2 = {(1↦1↦1↦2),(1↦1↦1↦3),(1↦1↦1↦4),(1↦1↦1↦5),(1↦1↦1↦6),(1↦1↦1↦7),(1↦1↦1↦8),(1↦1↦1↦9),(1↦1↦2↦3),(1↦1↦2↦4),(1↦1↦2↦5),(1↦1↦2↦6),(1↦1↦2↦7),(1↦1↦2↦8),(1↦1↦2↦9),(1↦1↦3↦4),(1↦1↦3↦5),(1↦1↦3↦6),(1↦1↦3↦7),(1↦1↦3↦8),(1↦1↦3↦9),(1↦1↦4↦5),(1↦1↦4↦6),(1↦1↦4↦7),(1↦1↦4↦8),(1↦1↦4↦9),(1↦1↦5↦6),(1↦1↦5↦7),(1↦1↦5↦8),(1↦1↦5↦9),(1↦1↦6↦7),(1↦1↦6↦8),(1↦1↦6↦9),(1↦1↦7↦8),(1↦1↦7↦9),(1↦1↦8↦9),(2↦2↦1↦2),(2↦2↦1↦3),(2↦2↦1↦4),(2↦2↦1↦5),(2↦2↦1↦6),(2↦2↦1↦7),(2↦2↦1↦8),(2↦2↦1↦9),(2↦2↦2↦3),(2↦2↦2↦4),(2↦2↦2↦5),(2↦2↦2↦6),(2↦2↦2↦7),(2↦2↦2↦8),(2↦2↦2↦9),(2↦2↦3↦4),(2↦2↦3↦5),(2↦2↦3↦6),(2↦2↦3↦7),(2↦2↦3↦8),(2↦2↦3↦9),(2↦2↦4↦5),(2↦2↦4↦6),(2↦2↦4↦7),(2↦2↦4↦8),(2↦2↦4↦9),(2↦2↦5↦6),(2↦2↦5↦7),(2↦2↦5↦8),(2↦2↦5↦9),(2↦2↦6↦7),(2↦2↦6↦8),(2↦2↦6↦9),(2↦2↦7↦8),(2↦2↦7↦9),(2↦2↦8↦9),(3↦3↦1↦2),(3↦3↦1↦3),(3↦3↦1↦4),(3↦3↦1↦5),(3↦3↦1↦6),(3↦3↦1↦7),(3↦3↦1↦8),(3↦3↦1↦9),(3↦3↦2↦3),(3↦3↦2↦4),(3↦3↦2↦5),(3↦3↦2↦6),(3↦3↦2↦7),(3↦3↦2↦8),(3↦3↦2↦9),(3↦3↦3↦4),(3↦3↦3↦5),(3↦3↦3↦6),(3↦3↦3↦7),(3↦3↦3↦8),(3↦3↦3↦9),(3↦3↦4↦5),(3↦3↦4↦6),(3↦3↦4↦7),(3↦3↦4↦8),(3↦3↦4↦9),(3↦3↦5↦6),(3↦3↦5↦7),(3↦3↦5↦8),(3↦3↦5↦9),(3↦3↦6↦7),(3↦3↦6↦8),(3↦3↦6↦9),(3↦3↦7↦8),(3↦3↦7↦9),(3↦3↦8↦9),(4↦4↦1↦2),(4↦4↦1↦3),(4↦4↦1↦4),(4↦4↦1↦5),(4↦4↦1↦6),(4↦4↦1↦7),(4↦4↦1↦8),(4↦4↦1↦9),(4↦4↦2↦3),(4↦4↦2↦4),(4↦4↦2↦5),(4↦4↦2↦6),(4↦4↦2↦7),(4↦4↦2↦8),(4↦4↦2↦9),(4↦4↦3↦4),(4↦4↦3↦5),(4↦4↦3↦6),(4↦4↦3↦7),(4↦4↦3↦8),(4↦4↦3↦9),(4↦4↦4↦5),(4↦4↦4↦6),(4↦4↦4↦7),(4↦4↦4↦8),(4↦4↦4↦9),(4↦4↦5↦6),(4↦4↦5↦7),(4↦4↦5↦8),(4↦4↦5↦9),(4↦4↦6↦7),(4↦4↦6↦8),(4↦4↦6↦9),(4↦4↦7↦8),(4↦4↦7↦9),(4↦4↦8↦9),(5↦5↦1↦2),(5↦5↦1↦3),(5↦5↦1↦4),(5↦5↦1↦5),(5↦5↦1↦6),(5↦5↦1↦7),(5↦5↦1↦8),(5↦5↦1↦9),(5↦5↦2↦3),(5↦5↦2↦4),(5↦5↦2↦5),(5↦5↦2↦6),(5↦5↦2↦7),(5↦5↦2↦8),(5↦5↦2↦9),(5↦5↦3↦4),(5↦5↦3↦5),(5↦5↦3↦6),(5↦5↦3↦7),(5↦5↦3↦8),(5↦5↦3↦9),(5↦5↦4↦5),(5↦5↦4↦6),(5↦5↦4↦7),(5↦5↦4↦8),(5↦5↦4↦9),(5↦5↦5↦6),(5↦5↦5↦7),(5↦5↦5↦8),(5↦5↦5↦9),(5↦5↦6↦7),(5↦5↦6↦8),(5↦5↦6↦9),(5↦5↦7↦8),(5↦5↦7↦9),(5↦5↦8↦9),(6↦6↦1↦2),(6↦6↦1↦3),(6↦6↦1↦4),(6↦6↦1↦5),(6↦6↦1↦6),(6↦6↦1↦7),(6↦6↦1↦8),(6↦6↦1↦9),(6↦6↦2↦3),(6↦6↦2↦4),(6↦6↦2↦5),(6↦6↦2↦6),(6↦6↦2↦7),(6↦6↦2↦8),(6↦6↦2↦9),(6↦6↦3↦4),(6↦6↦3↦5),(6↦6↦3↦6),(6↦6↦3↦7),(6↦6↦3↦8),(6↦6↦3↦9),(6↦6↦4↦5),(6↦6↦4↦6),(6↦6↦4↦7),(6↦6↦4↦8),(6↦6↦4↦9),(6↦6↦5↦6),(6↦6↦5↦7),(6↦6↦5↦8),(6↦6↦5↦9),(6↦6↦6↦7),(6↦6↦6↦8),(6↦6↦6↦9),(6↦6↦7↦8),(6↦6↦7↦9),(6↦6↦8↦9),(7↦7↦1↦2),(7↦7↦1↦3),(7↦7↦1↦4),(7↦7↦1↦5),(7↦7↦1↦6),(7↦7↦1↦7),(7↦7↦1↦8),(7↦7↦1↦9),(7↦7↦2↦3),(7↦7↦2↦4),(7↦7↦2↦5),(7↦7↦2↦6),(7↦7↦2↦7),(7↦7↦2↦8),(7↦7↦2↦9),(7↦7↦3↦4),(7↦7↦3↦5),(7↦7↦3↦6),(7↦7↦3↦7),(7↦7↦3↦8),(7↦7↦3↦9),(7↦7↦4↦5),(7↦7↦4↦6),(7↦7↦4↦7),(7↦7↦4↦8),(7↦7↦4↦9),(7↦7↦5↦6),(7↦7↦5↦7),(7↦7↦5↦8),(7↦7↦5↦9),(7↦7↦6↦7),(7↦7↦6↦8),(7↦7↦6↦9),(7↦7↦7↦8),(7↦7↦7↦9),(7↦7↦8↦9),(8↦8↦1↦2),(8↦8↦1↦3),(8↦8↦1↦4),(8↦8↦1↦5),(8↦8↦1↦6),(8↦8↦1↦7),(8↦8↦1↦8),(8↦8↦1↦9),(8↦8↦2↦3),(8↦8↦2↦4),(8↦8↦2↦5),(8↦8↦2↦6),(8↦8↦2↦7),(8↦8↦2↦8),(8↦8↦2↦9),(8↦8↦3↦4),(8↦8↦3↦5),(8↦8↦3↦6),(8↦8↦3↦7),(8↦8↦3↦8),(8↦8↦3↦9),(8↦8↦4↦5),(8↦8↦4↦6),(8↦8↦4↦7),(8↦8↦4↦8),(8↦8↦4↦9),(8↦8↦5↦6),(8↦8↦5↦7),(8↦8↦5↦8),(8↦8↦5↦9),(8↦8↦6↦7),(8↦8↦6↦8),(8↦8↦6↦9),(8↦8↦7↦8),(8↦8↦7↦9),(8↦8↦8↦9),(9↦9↦1↦2),(9↦9↦1↦3),(9↦9↦1↦4),(9↦9↦1↦5),(9↦9↦1↦6),(9↦9↦1↦7),(9↦9↦1↦8),(9↦9↦1↦9),(9↦9↦2↦3),(9↦9↦2↦4),(9↦9↦2↦5),(9↦9↦2↦6),(9↦9↦2↦7),(9↦9↦2↦8),(9↦9↦2↦9),(9↦9↦3↦4),(9↦9↦3↦5),(9↦9↦3↦6),(9↦9↦3↦7),(9↦9↦3↦8),(9↦9↦3↦9),(9↦9↦4↦5),(9↦9↦4↦6),(9↦9↦4↦7),(9↦9↦4↦8),(9↦9↦4↦9),(9↦9↦5↦6),(9↦9↦5↦7),(9↦9↦5↦8),(9↦9↦5↦9),(9↦9↦6↦7),(9↦9↦6↦8),(9↦9↦6↦9),(9↦9↦7↦8),(9↦9↦7↦9),(9↦9↦8↦9)}
Board = {(1↦{(1↦7),(2↦8),(3↦1),(4↦1),(5↦1),(6↦1),(7↦1),(8↦1),(9↦1)}),(2↦{(1↦9),(2↦1),(3↦1),(4↦1),(5↦1),(6↦1),(7↦1),(8↦1),(9↦1)}),(3↦{(1↦1),(2↦1),(3↦1),(4↦1),(5↦1),(6↦1),(7↦1),(8↦1),(9↦1)}),(4↦{(1↦1),(2↦1),(3↦1),(4↦1),(5↦1),(6↦1),(7↦1),(8↦1),(9↦1)}),(5↦{(1↦1),(2↦1),(3↦1),(4↦1),(5↦1),(6↦1),(7↦1),(8↦1),(9↦1)}),(6↦{(1↦1),(2↦1),(3↦1),(4↦1),(5↦1),(6↦1),(7↦1),(8↦1),(9↦1)}),(7↦{(1↦1),(2↦1),(3↦1),(4↦1),(5↦1),(6↦1),(7↦1),(8↦1),(9↦1)}),(8↦{(1↦1),(2↦1),(3↦1),(4↦1),(5↦1),(6↦1),(7↦1),(8↦1),(9↦1)}),(9↦{(1↦1),(2↦1),(3↦1),(4↦1),(5↦1),(6↦1),(7↦1),(8↦1),(9↦1)})}
DOM = {1,2,3,4,5,6,7,8,9}
Diff1 = {(1↦2↦1↦1),(1↦2↦2↦2),(1↦2↦3↦3),(1↦2↦4↦4),(1↦2↦5↦5),(1↦2↦6↦6),(1↦2↦7↦7),(1↦2↦8↦8),(1↦2↦9↦9),(1↦3↦1↦1),(1↦3↦2↦2),(1↦3↦3↦3),(1↦3↦4↦4),(1↦3↦5↦5),(1↦3↦6↦6),(1↦3↦7↦7),(1↦3↦8↦8),(1↦3↦9↦9),(1↦4↦1↦1),(1↦4↦2↦2),(1↦4↦3↦3),(1↦4↦4↦4),(1↦4↦5↦5),(1↦4↦6↦6),(1↦4↦7↦7),(1↦4↦8↦8),(1↦4↦9↦9),(1↦5↦1↦1),(1↦5↦2↦2),(1↦5↦3↦3),(1↦5↦4↦4),(1↦5↦5↦5),(1↦5↦6↦6),(1↦5↦7↦7),(1↦5↦8↦8),(1↦5↦9↦9),(1↦6↦1↦1),(1↦6↦2↦2),(1↦6↦3↦3),(1↦6↦4↦4),(1↦6↦5↦5),(1↦6↦6↦6),(1↦6↦7↦7),(1↦6↦8↦8),(1↦6↦9↦9),(1↦7↦1↦1),(1↦7↦2↦2),(1↦7↦3↦3),(1↦7↦4↦4),(1↦7↦5↦5),(1↦7↦6↦6),(1↦7↦7↦7),(1↦7↦8↦8),(1↦7↦9↦9),(1↦8↦1↦1),(1↦8↦2↦2),(1↦8↦3↦3),(1↦8↦4↦4),(1↦8↦5↦5),(1↦8↦6↦6),(1↦8↦7↦7),(1↦8↦8↦8),(1↦8↦9↦9),(1↦9↦1↦1),(1↦9↦2↦2),(1↦9↦3↦3),(1↦9↦4↦4),(1↦9↦5↦5),(1↦9↦6↦6),(1↦9↦7↦7),(1↦9↦8↦8),(1↦9↦9↦9),(2↦3↦1↦1),(2↦3↦2↦2),(2↦3↦3↦3),(2↦3↦4↦4),(2↦3↦5↦5),(2↦3↦6↦6),(2↦3↦7↦7),(2↦3↦8↦8),(2↦3↦9↦9),(2↦4↦1↦1),(2↦4↦2↦2),(2↦4↦3↦3),(2↦4↦4↦4),(2↦4↦5↦5),(2↦4↦6↦6),(2↦4↦7↦7),(2↦4↦8↦8),(2↦4↦9↦9),(2↦5↦1↦1),(2↦5↦2↦2),(2↦5↦3↦3),(2↦5↦4↦4),(2↦5↦5↦5),(2↦5↦6↦6),(2↦5↦7↦7),(2↦5↦8↦8),(2↦5↦9↦9),(2↦6↦1↦1),(2↦6↦2↦2),(2↦6↦3↦3),(2↦6↦4↦4),(2↦6↦5↦5),(2↦6↦6↦6),(2↦6↦7↦7),(2↦6↦8↦8),(2↦6↦9↦9),(2↦7↦1↦1),(2↦7↦2↦2),(2↦7↦3↦3),(2↦7↦4↦4),(2↦7↦5↦5),(2↦7↦6↦6),(2↦7↦7↦7),(2↦7↦8↦8),(2↦7↦9↦9),(2↦8↦1↦1),(2↦8↦2↦2),(2↦8↦3↦3),(2↦8↦4↦4),(2↦8↦5↦5),(2↦8↦6↦6),(2↦8↦7↦7),(2↦8↦8↦8),(2↦8↦9↦9),(2↦9↦1↦1),(2↦9↦2↦2),(2↦9↦3↦3),(2↦9↦4↦4),(2↦9↦5↦5),(2↦9↦6↦6),(2↦9↦7↦7),(2↦9↦8↦8),(2↦9↦9↦9),(3↦4↦1↦1),(3↦4↦2↦2),(3↦4↦3↦3),(3↦4↦4↦4),(3↦4↦5↦5),(3↦4↦6↦6),(3↦4↦7↦7),(3↦4↦8↦8),(3↦4↦9↦9),(3↦5↦1↦1),(3↦5↦2↦2),(3↦5↦3↦3),(3↦5↦4↦4),(3↦5↦5↦5),(3↦5↦6↦6),(3↦5↦7↦7),(3↦5↦8↦8),(3↦5↦9↦9),(3↦6↦1↦1),(3↦6↦2↦2),(3↦6↦3↦3),(3↦6↦4↦4),(3↦6↦5↦5),(3↦6↦6↦6),(3↦6↦7↦7),(3↦6↦8↦8),(3↦6↦9↦9),(3↦7↦1↦1),(3↦7↦2↦2),(3↦7↦3↦3),(3↦7↦4↦4),(3↦7↦5↦5),(3↦7↦6↦6),(3↦7↦7↦7),(3↦7↦8↦8),(3↦7↦9↦9),(3↦8↦1↦1),(3↦8↦2↦2),(3↦8↦3↦3),(3↦8↦4↦4),(3↦8↦5↦5),(3↦8↦6↦6),(3↦8↦7↦7),(3↦8↦8↦8),(3↦8↦9↦9),(3↦9↦1↦1),(3↦9↦2↦2),(3↦9↦3↦3),(3↦9↦4↦4),(3↦9↦5↦5),(3↦9↦6↦6),(3↦9↦7↦7),(3↦9↦8↦8),(3↦9↦9↦9),(4↦5↦1↦1),(4↦5↦2↦2),(4↦5↦3↦3),(4↦5↦4↦4),(4↦5↦5↦5),(4↦5↦6↦6),(4↦5↦7↦7),(4↦5↦8↦8),(4↦5↦9↦9),(4↦6↦1↦1),(4↦6↦2↦2),(4↦6↦3↦3),(4↦6↦4↦4),(4↦6↦5↦5),(4↦6↦6↦6),(4↦6↦7↦7),(4↦6↦8↦8),(4↦6↦9↦9),(4↦7↦1↦1),(4↦7↦2↦2),(4↦7↦3↦3),(4↦7↦4↦4),(4↦7↦5↦5),(4↦7↦6↦6),(4↦7↦7↦7),(4↦7↦8↦8),(4↦7↦9↦9),(4↦8↦1↦1),(4↦8↦2↦2),(4↦8↦3↦3),(4↦8↦4↦4),(4↦8↦5↦5),(4↦8↦6↦6),(4↦8↦7↦7),(4↦8↦8↦8),(4↦8↦9↦9),(4↦9↦1↦1),(4↦9↦2↦2),(4↦9↦3↦3),(4↦9↦4↦4),(4↦9↦5↦5),(4↦9↦6↦6),(4↦9↦7↦7),(4↦9↦8↦8),(4↦9↦9↦9),(5↦6↦1↦1),(5↦6↦2↦2),(5↦6↦3↦3),(5↦6↦4↦4),(5↦6↦5↦5),(5↦6↦6↦6),(5↦6↦7↦7),(5↦6↦8↦8),(5↦6↦9↦9),(5↦7↦1↦1),(5↦7↦2↦2),(5↦7↦3↦3),(5↦7↦4↦4),(5↦7↦5↦5),(5↦7↦6↦6),(5↦7↦7↦7),(5↦7↦8↦8),(5↦7↦9↦9),(5↦8↦1↦1),(5↦8↦2↦2),(5↦8↦3↦3),(5↦8↦4↦4),(5↦8↦5↦5),(5↦8↦6↦6),(5↦8↦7↦7),(5↦8↦8↦8),(5↦8↦9↦9),(5↦9↦1↦1),(5↦9↦2↦2),(5↦9↦3↦3),(5↦9↦4↦4),(5↦9↦5↦5),(5↦9↦6↦6),(5↦9↦7↦7),(5↦9↦8↦8),(5↦9↦9↦9),(6↦7↦1↦1),(6↦7↦2↦2),(6↦7↦3↦3),(6↦7↦4↦4),(6↦7↦5↦5),(6↦7↦6↦6),(6↦7↦7↦7),(6↦7↦8↦8),(6↦7↦9↦9),(6↦8↦1↦1),(6↦8↦2↦2),(6↦8↦3↦3),(6↦8↦4↦4),(6↦8↦5↦5),(6↦8↦6↦6),(6↦8↦7↦7),(6↦8↦8↦8),(6↦8↦9↦9),(6↦9↦1↦1),(6↦9↦2↦2),(6↦9↦3↦3),(6↦9↦4↦4),(6↦9↦5↦5),(6↦9↦6↦6),(6↦9↦7↦7),(6↦9↦8↦8),(6↦9↦9↦9),(7↦8↦1↦1),(7↦8↦2↦2),(7↦8↦3↦3),(7↦8↦4↦4),(7↦8↦5↦5),(7↦8↦6↦6),(7↦8↦7↦7),(7↦8↦8↦8),(7↦8↦9↦9),(7↦9↦1↦1),(7↦9↦2↦2),(7↦9↦3↦3),(7↦9↦4↦4),(7↦9↦5↦5),(7↦9↦6↦6),(7↦9↦7↦7),(7↦9↦8↦8),(7↦9↦9↦9),(8↦9↦1↦1),(8↦9↦2↦2),(8↦9↦3↦3),(8↦9↦4↦4),(8↦9↦5↦5),(8↦9↦6↦6),(8↦9↦7↦7),(8↦9↦8↦8),(8↦9↦9↦9)}
Diff = ∅
SUBSQ = {{1,2,3},{4,5,6},{7,8,9}}
%% Cell type:code id: tags:
``` prob
:init
```
%% Output
Machine initialised using operation 0: $initialise_machine()
%% Cell type:code id: tags:
``` prob
:show
```
%% Output
<table style="font-family:monospace"><tbody>
</tbody></table>
<Animation function visualisation>
%% Cell type:code id: tags:
``` prob
```
Untitled.ipynb 0 → 100644
+ 347
− 0
View file @ 83dcdd35
%% Cell type:markdown id: tags:
# The Jobs Puzzle
Based on *Michael Leuschel, David Schneider. Towards B as a High-Level Constraint Modeling Language. In Yamine Ait Amer, Klaus-Dieter Schewe (ed.): Abstract State Machines, Alloy, B, TLA, VDM, and Z, Springer Berlin Heidelberg, 8477: 101-116, 2014.*
This puzzle was originally published in 1984 by [Wos et al., 1984](https://www.mcs.anl.gov/research/projects/AR/book1.html) as part of a collection of puzzles for automatic reasoners. A reference implementation of the puzzle, by one of the authors of the book, using [OTTER, 2003](https://arxiv.org/abs/cs/0310056).
The puzzle consists of eight statements that describe the problem domain and provide some constraints on the elements of the domain. The problem is about a set of people and a set of jobs; the question posed by the puzzle is: who holds which job? The text of the puzzle as presented in "The jobs puzzle: A challenge for logical expressibility and automated reasoning."[S. C. Shapiro, 2011](https://cse.buffalo.edu/~shapiro/Papers/SS11-06-017.pdf) is as follows:
* There are four people: Roberta, Thelma, Steve, and Pete.
* Among them, they hold eight different jobs.
* Each holds exactly two jobs.
* The jobs are: chef, guard, nurse, clerk, police officer (gender not implied), teacher, actor, and boxer.
* The job of nurse is held by a male.
* The husband of the chef is the clerk.
* Roberta is not a boxer.
* Pete has no education past the ninth grade.
* Roberta, the chef, and the police officer went golfing together.
What makes this puzzle interesting for automatic reasoners, is that not all the information required to solve the puzzle is provided explicitly in the text.
The puzzle can only be solved if certain implicit assumptions about the world are taken into account, such as: the names in the puzzle denote gender or that some of the job names imply the gender of the person that holds it.
%% Cell type:markdown id: tags:
## Shapiro's Challenge
Shapiro, following the original authors' remarks, that formalizing the puzzle was at times hard and tendious, identified three challenges posed by the puat times hard and tedious, identified three challenges posed by the puzzle with regard to automatic reasoners. According to Shapiro, the challenges posed by the jobs puzzle are to:
1. formalize it in a non-difficult, non-tedious way
2. formalize it in a way that adheres closely to the English statement of the puzzle
3. have an automated general-purpose commonsense reasoner that can accept that formalization and solve the puzzle quickly.
Any formalization also needs to encode the implicit knowledge used to solve the puzzle for the automatic reasoners while still trying to satisfy the aspects mentioned above. Addressing this challenge makes this puzzle a good case-study for the expressiveness of B to formalize such a problem.
%% Cell type:markdown id: tags:
## A Solution to the Jobs Puzzle using B
The B encoding of the puzzle uses plain predicate logic,
combined with set theory and arithmetic. We will show how this
enables a very concise encoding of the problem, staying very close to the natural language requirements. Moreover, the puzzle can be quickly solved using the constraint solving capabilities of ProB. Following the order of the sentences in the puzzle we will discuss one or more possibilities to formalize them using B.
To express "*There are four people: Roberta, Thelma, Steve, and Pete*" we define a set of people, that holds the list of names:
%% Cell type:code id: tags:
``` prob
:let PEOPLE {"Roberta", "Thelma", "Steve", "Pete"}
```
%% Cell type:markdown id: tags:
We are using strings here to describe the elements of the set. This has the advantage, that the elements of the set are implicitly different.
Alternatively, we could use enumerated or deferred sets defined in the SETS section of a B machine. As stated above we need some additional information that is not included in the puzzle to solve it.
The first bit of information is that the names used in the puzzle imply the gender. In order to express this information we create two sets, MALE and FEMALE which are subsets of PEOPLE and contain the corresponding names.
%% Cell type:code id: tags:
``` prob
:let FEMALE {"Roberta", "Thelma"}
```
%% Output
$\{\text{"Roberta"},\text{"Thelma"}\}$
{"Roberta","Thelma"}
%% Cell type:code id: tags:
``` prob
:let MALE {"Steve", "Pete"}
```
%% Output
$\{\text{"Pete"},\text{"Steve"}\}$
{"Pete","Steve"}
%% Cell type:markdown id: tags:
The next statement of the puzzle is: "*among them, they hold eight different jobs*". This can be formalized in B using a function that maps from a job to the corresponding person that holds this job using a total surjection from JOBS to PEOPLE.
To use that statement, however we have to define JOBS, or the fourth statement.
%% Cell type:code id: tags:
``` prob
:let JOBS {"chef", "guard", "nurse", "clerk", "police", "teacher", "actor", "boxer"}
```
%% Output
$\{\text{"actor"},\text{"boxer"},\text{"chef"},\text{"clerk"},\text{"guard"},\text{"nurse"},\text{"police"},\text{"teacher"}\}$
{"actor","boxer","chef","clerk","guard","nurse","police","teacher"}
%% Cell type:markdown id: tags:
Now we can see what Holds Job will do.
%% Cell type:code id: tags:
``` prob
HoldsJob : JOBS -->> PEOPLE
```
%% Output
$\mathit{TRUE}$
**Solution:**
* $\mathit{HoldsJob} = \{(\text{"actor"}\mapsto\text{"Steve"}),(\text{"boxer"}\mapsto\text{"Thelma"}),(\text{"chef"}\mapsto\text{"Pete"}),(\text{"clerk"}\mapsto\text{"Pete"}),(\text{"guard"}\mapsto\text{"Pete"}),(\text{"nurse"}\mapsto\text{"Pete"}),(\text{"police"}\mapsto\text{"Pete"}),(\text{"teacher"}\mapsto\text{"Roberta"})\}$
* $\mathit{JOBS} = \{\text{"actor"},\text{"boxer"},\text{"chef"},\text{"clerk"},\text{"guard"},\text{"nurse"},\text{"police"},\text{"teacher"}\}$
* $\mathit{PEOPLE} = \{\text{"Pete"},\text{"Roberta"},\text{"Steve"},\text{"Thelma"}\}$
* $\mathit{MALE} = \{\text{"Pete"},\text{"Steve"}\}$
* $\mathit{FEMALE} = \{\text{"Roberta"},\text{"Thelma"}\}$
TRUE
Solution:
HoldsJob = {("actor"↦"Steve"),("boxer"↦"Thelma"),("chef"↦"Pete"),("clerk"↦"Pete"),("guard"↦"Pete"),("nurse"↦"Pete"),("police"↦"Pete"),("teacher"↦"Roberta")}
JOBS = {"actor","boxer","chef","clerk","guard","nurse","police","teacher"}
PEOPLE = {"Pete","Roberta","Steve","Thelma"}
MALE = {"Pete","Steve"}
FEMALE = {"Roberta","Thelma"}
%% Cell type:markdown id: tags:
Since we have not yet added any additional information, the Jobs are just randomly assigned to each Person.
Although redundant, as we will see below, to express “*Among them, they hold eight different jobs*” we can add the assertion that the cardinality of HoldsJob is 8.
This is possible, because in B functions and relations can be treated as sets of pairs, where each pair consists of an element of the domain and the corresponding element from the range of the relation.
%% Cell type:code id: tags:
``` prob
HoldsJob : JOBS -->> PEOPLE & card(HoldsJob) = 8
```
%% Output
$\mathit{TRUE}$
**Solution:**
* $\mathit{HoldsJob} = \{(\text{"actor"}\mapsto\text{"Steve"}),(\text{"boxer"}\mapsto\text{"Thelma"}),(\text{"chef"}\mapsto\text{"Pete"}),(\text{"clerk"}\mapsto\text{"Pete"}),(\text{"guard"}\mapsto\text{"Pete"}),(\text{"nurse"}\mapsto\text{"Pete"}),(\text{"police"}\mapsto\text{"Pete"}),(\text{"teacher"}\mapsto\text{"Roberta"})\}$
* $\mathit{JOBS} = \{\text{"actor"},\text{"boxer"},\text{"chef"},\text{"clerk"},\text{"guard"},\text{"nurse"},\text{"police"},\text{"teacher"}\}$
* $\mathit{PEOPLE} = \{\text{"Pete"},\text{"Roberta"},\text{"Steve"},\text{"Thelma"}\}$
* $\mathit{MALE} = \{\text{"Pete"},\text{"Steve"}\}$
* $\mathit{FEMALE} = \{\text{"Roberta"},\text{"Thelma"}\}$
TRUE
Solution:
HoldsJob = {("actor"↦"Steve"),("boxer"↦"Thelma"),("chef"↦"Pete"),("clerk"↦"Pete"),("guard"↦"Pete"),("nurse"↦"Pete"),("police"↦"Pete"),("teacher"↦"Roberta")}
JOBS = {"actor","boxer","chef","clerk","guard","nurse","police","teacher"}
PEOPLE = {"Pete","Roberta","Steve","Thelma"}
MALE = {"Pete","Steve"}
FEMALE = {"Roberta","Thelma"}
%% Cell type:markdown id: tags:
Constraining the jobs each person holds, the puzzle states: “*Each holds exactly two jobs*”. To express this we use the inverse relation of HoldsJob, it maps a PERSON to the JOBS associated to her. The inverse function or relation is expressed in B using the ~ operator.
For readability we assign the inverse of HoldsJob to a variable called JobsOf. JobsOf is in this case is a relation, because, as stated above, each person holds two jobs.
First of all, we have to add HoldsJob to our globals, however.
%% Cell type:code id: tags:
``` prob
:let HoldsJob JOBS -->> PEOPLE
```
%% Output
de.prob.animator.domainobjects.EvaluationException: de.be4.classicalb.core.parser.exceptions.BCompoundException: [2,26] expecting: identifier literal
%% Cell type:markdown id: tags:
Because JobsOf is a relation and not a function, in order to read the values, we need to use B’s relational image operator. This operator maps a subset of the domain to a subset of the range, instead of a single value. To read the jobs Steve holds, the relational image of JobsOf is used as shown below:
%% Cell type:code id: tags:
``` prob
:let card(HoldsJob) 8
```
%% Output
$8$
8
%% Cell type:code id: tags:
``` prob
:let JobsOf HoldsJob~
```
%% Output
de.prob.animator.domainobjects.EvaluationException: de.be4.classicalb.core.parser.exceptions.BCompoundException: [2,26] expecting: identifier literal
%% Cell type:code id: tags:
``` prob
```
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