%------------------------------------------------------------------------------
% File : SWW645_2 : TPTP v8.2.0. Released v6.1.0.
% Domain : Software Verification
% Problem : Sudoku-T-WP parameter classical sudoku
% Version : Especial : Let and conditional terms encoded away.
% English :
% Refs : [Fil14] Filliatre (2014), Email to Geoff Sutcliffe
% : [BF+] Bobot et al. (URL), Toccata: Certified Programs and Cert
% Source : [Fil14]
% Names : sudoku-T-WP_parameter_classical_sudoku [Fil14]
% Status : Theorem
% Rating : 1.00 v6.3.0, 0.86 v6.2.0, 1.00 v6.1.0
% Syntax : Number of formulae : 116 ( 33 unt; 57 typ; 0 def)
% Number of atoms : 1230 ( 310 equ)
% Maximal formula atoms : 1093 ( 10 avg)
% Number of connectives : 1177 ( 6 ~; 1 |; 855 &)
% ( 14 <=>; 301 =>; 0 <=; 0 <~>)
% Maximal formula depth : 1094 ( 24 avg)
% Maximal term depth : 8 ( 1 avg)
% Number arithmetic : 3124 ( 851 atm; 10 fun;2227 num; 36 var)
% Number of types : 9 ( 7 usr; 1 ari)
% Number of type conns : 89 ( 41 >; 48 *; 0 +; 0 <<)
% Number of predicates : 18 ( 15 usr; 0 prp; 1-4 aty)
% Number of functors : 119 ( 35 usr; 91 con; 0-6 aty)
% Number of variables : 449 ( 449 !; 0 ?; 449 :)
% SPC : TF0_THM_EQU_ARI
% Comments :
%------------------------------------------------------------------------------
tff(uni,type,
uni: $tType ).
tff(ty,type,
ty: $tType ).
tff(sort,type,
sort1: ( ty * uni ) > $o ).
tff(witness,type,
witness1: ty > uni ).
tff(witness_sort1,axiom,
! [A: ty] : sort1(A,witness1(A)) ).
tff(int,type,
int: ty ).
tff(real,type,
real: ty ).
tff(bool,type,
bool1: $tType ).
tff(bool1,type,
bool: ty ).
tff(true,type,
true1: bool1 ).
tff(false,type,
false1: bool1 ).
tff(match_bool,type,
match_bool1: ( ty * bool1 * uni * uni ) > uni ).
tff(match_bool_sort1,axiom,
! [A: ty,X: bool1,X1: uni,X2: uni] : sort1(A,match_bool1(A,X,X1,X2)) ).
tff(match_bool_True,axiom,
! [A: ty,Z: uni,Z1: uni] :
( sort1(A,Z)
=> ( match_bool1(A,true1,Z,Z1) = Z ) ) ).
tff(match_bool_False,axiom,
! [A: ty,Z: uni,Z1: uni] :
( sort1(A,Z1)
=> ( match_bool1(A,false1,Z,Z1) = Z1 ) ) ).
tff(true_False,axiom,
true1 != false1 ).
tff(bool_inversion,axiom,
! [U: bool1] :
( ( U = true1 )
| ( U = false1 ) ) ).
tff(tuple0,type,
tuple02: $tType ).
tff(tuple01,type,
tuple0: ty ).
tff(tuple02,type,
tuple03: tuple02 ).
tff(tuple0_inversion,axiom,
! [U: tuple02] : U = tuple03 ).
tff(qtmark,type,
qtmark: ty ).
tff(compatOrderMult,axiom,
! [X: $int,Y: $int,Z: $int] :
( $lesseq(X,Y)
=> ( $lesseq(0,Z)
=> $lesseq($product(X,Z),$product(Y,Z)) ) ) ).
tff(map,type,
map: ( ty * ty ) > ty ).
tff(get,type,
get: ( ty * ty * uni * uni ) > uni ).
tff(get_sort2,axiom,
! [A: ty,B: ty,X: uni,X1: uni] : sort1(B,get(B,A,X,X1)) ).
tff(set,type,
set: ( ty * ty * uni * uni * uni ) > uni ).
tff(set_sort2,axiom,
! [A: ty,B: ty,X: uni,X1: uni,X2: uni] : sort1(map(A,B),set(B,A,X,X1,X2)) ).
tff(select_eq,axiom,
! [A: ty,B: ty,M: uni,A1: uni,A2: uni,B1: uni] :
( sort1(B,B1)
=> ( ( A1 = A2 )
=> ( get(B,A,set(B,A,M,A1,B1),A2) = B1 ) ) ) ).
tff(select_neq,axiom,
! [A: ty,B: ty,M: uni,A1: uni,A2: uni] :
( sort1(A,A1)
=> ( sort1(A,A2)
=> ! [B1: uni] :
( ( A1 != A2 )
=> ( get(B,A,set(B,A,M,A1,B1),A2) = get(B,A,M,A2) ) ) ) ) ).
tff(const1,type,
const: ( ty * ty * uni ) > uni ).
tff(const_sort1,axiom,
! [A: ty,B: ty,X: uni] : sort1(map(A,B),const(B,A,X)) ).
tff(const,axiom,
! [A: ty,B: ty,B1: uni,A1: uni] :
( sort1(B,B1)
=> ( get(B,A,const(B,A,B1),A1) = B1 ) ) ).
tff(is_index,type,
is_index1: $int > $o ).
tff(is_index_def,axiom,
! [I: $int] :
( is_index1(I)
<=> ( $lesseq(0,I)
& $less(I,81) ) ) ).
tff(map_int_int,type,
map_int_int: $tType ).
tff(valid_values,type,
valid_values1: map_int_int > $o ).
tff(t2tb,type,
t2tb: map_int_int > uni ).
tff(t2tb_sort,axiom,
! [X: map_int_int] : sort1(map(int,int),t2tb(X)) ).
tff(tb2t,type,
tb2t: uni > map_int_int ).
tff(bridgeL,axiom,
! [I: map_int_int] : tb2t(t2tb(I)) = I ).
tff(bridgeR,axiom,
! [J: uni] : t2tb(tb2t(J)) = J ).
tff(t2tb1,type,
t2tb1: $int > uni ).
tff(t2tb_sort1,axiom,
! [X: $int] : sort1(int,t2tb1(X)) ).
tff(tb2t1,type,
tb2t1: uni > $int ).
tff(bridgeL1,axiom,
! [I: $int] : tb2t1(t2tb1(I)) = I ).
tff(bridgeR1,axiom,
! [J: uni] : t2tb1(tb2t1(J)) = J ).
tff(valid_values_def,axiom,
! [G: map_int_int] :
( valid_values1(G)
<=> ! [I: $int] :
( is_index1(I)
=> ( $lesseq(0,tb2t1(get(int,int,t2tb(G),t2tb1(I))))
& $lesseq(tb2t1(get(int,int,t2tb(G),t2tb1(I))),9) ) ) ) ).
tff(grid_eq_sub1,type,
grid_eq_sub1: ( map_int_int * map_int_int * $int * $int ) > $o ).
tff(grid_eq_sub_def,axiom,
! [G1: map_int_int,G2: map_int_int,A: $int,B: $int] :
( grid_eq_sub1(G1,G2,A,B)
<=> ! [J: $int] :
( ( $lesseq(A,J)
& $less(J,B) )
=> ( tb2t1(get(int,int,t2tb(G1),t2tb1(J))) = tb2t1(get(int,int,t2tb(G2),t2tb1(J))) ) ) ) ).
tff(grid_eq_sub,axiom,
! [G1: map_int_int,G2: map_int_int,A: $int,B: $int] :
( ( $lesseq(0,A)
& $lesseq(A,81)
& $lesseq(0,B)
& $lesseq(B,81)
& grid_eq_sub1(G1,G2,0,81) )
=> grid_eq_sub1(G1,G2,A,B) ) ).
tff(array,type,
array: ty > ty ).
tff(mk_array,type,
mk_array1: ( ty * $int * uni ) > uni ).
tff(mk_array_sort1,axiom,
! [A: ty,X: $int,X1: uni] : sort1(array(A),mk_array1(A,X,X1)) ).
tff(length,type,
length1: ( ty * uni ) > $int ).
tff(length_def1,axiom,
! [A: ty,U: $int,U1: uni] : length1(A,mk_array1(A,U,U1)) = U ).
tff(elts,type,
elts: ( ty * uni ) > uni ).
tff(elts_sort1,axiom,
! [A: ty,X: uni] : sort1(map(int,A),elts(A,X)) ).
tff(elts_def1,axiom,
! [A: ty,U: $int,U1: uni] :
( sort1(map(int,A),U1)
=> ( elts(A,mk_array1(A,U,U1)) = U1 ) ) ).
tff(array_inversion1,axiom,
! [A: ty,U: uni] : U = mk_array1(A,length1(A,U),elts(A,U)) ).
tff(get1,type,
get2: ( ty * uni * $int ) > uni ).
tff(get_sort3,axiom,
! [A: ty,X: uni,X1: $int] : sort1(A,get2(A,X,X1)) ).
tff(get_def,axiom,
! [A: ty,A1: uni,I: $int] : get2(A,A1,I) = get(A,int,elts(A,A1),t2tb1(I)) ).
tff(set1,type,
set2: ( ty * uni * $int * uni ) > uni ).
tff(set_sort3,axiom,
! [A: ty,X: uni,X1: $int,X2: uni] : sort1(array(A),set2(A,X,X1,X2)) ).
tff(set_def,axiom,
! [A: ty,A1: uni,I: $int,V: uni] : set2(A,A1,I,V) = mk_array1(A,length1(A,A1),set(A,int,elts(A,A1),t2tb1(I),V)) ).
tff(make,type,
make1: ( ty * $int * uni ) > uni ).
tff(make_sort1,axiom,
! [A: ty,X: $int,X1: uni] : sort1(array(A),make1(A,X,X1)) ).
tff(make_def,axiom,
! [A: ty,N: $int,V: uni] : make1(A,N,V) = mk_array1(A,N,const(A,int,V)) ).
tff(sudoku_chunks,type,
sudoku_chunks1: $tType ).
tff(sudoku_chunks1,type,
sudoku_chunks: ty ).
tff(array_int,type,
array_int: $tType ).
tff(mk_sudoku_chunks,type,
mk_sudoku_chunks1: ( array_int * array_int * array_int * array_int * array_int * array_int ) > sudoku_chunks1 ).
tff(column_start,type,
column_start1: sudoku_chunks1 > array_int ).
tff(column_start_def1,axiom,
! [U: array_int,U1: array_int,U2: array_int,U3: array_int,U4: array_int,U5: array_int] : column_start1(mk_sudoku_chunks1(U,U1,U2,U3,U4,U5)) = U ).
tff(column_offsets,type,
column_offsets1: sudoku_chunks1 > array_int ).
tff(column_offsets_def1,axiom,
! [U: array_int,U1: array_int,U2: array_int,U3: array_int,U4: array_int,U5: array_int] : column_offsets1(mk_sudoku_chunks1(U,U1,U2,U3,U4,U5)) = U1 ).
tff(row_start,type,
row_start1: sudoku_chunks1 > array_int ).
tff(row_start_def1,axiom,
! [U: array_int,U1: array_int,U2: array_int,U3: array_int,U4: array_int,U5: array_int] : row_start1(mk_sudoku_chunks1(U,U1,U2,U3,U4,U5)) = U2 ).
tff(row_offsets,type,
row_offsets1: sudoku_chunks1 > array_int ).
tff(row_offsets_def1,axiom,
! [U: array_int,U1: array_int,U2: array_int,U3: array_int,U4: array_int,U5: array_int] : row_offsets1(mk_sudoku_chunks1(U,U1,U2,U3,U4,U5)) = U3 ).
tff(square_start,type,
square_start1: sudoku_chunks1 > array_int ).
tff(square_start_def1,axiom,
! [U: array_int,U1: array_int,U2: array_int,U3: array_int,U4: array_int,U5: array_int] : square_start1(mk_sudoku_chunks1(U,U1,U2,U3,U4,U5)) = U4 ).
tff(square_offsets,type,
square_offsets1: sudoku_chunks1 > array_int ).
tff(square_offsets_def1,axiom,
! [U: array_int,U1: array_int,U2: array_int,U3: array_int,U4: array_int,U5: array_int] : square_offsets1(mk_sudoku_chunks1(U,U1,U2,U3,U4,U5)) = U5 ).
tff(sudoku_chunks_inversion1,axiom,
! [U: sudoku_chunks1] : U = mk_sudoku_chunks1(column_start1(U),column_offsets1(U),row_start1(U),row_offsets1(U),square_start1(U),square_offsets1(U)) ).
tff(chunk_valid_indexes,type,
chunk_valid_indexes1: ( array_int * array_int ) > $o ).
tff(t2tb2,type,
t2tb2: array_int > uni ).
tff(t2tb_sort2,axiom,
! [X: array_int] : sort1(array(int),t2tb2(X)) ).
tff(tb2t2,type,
tb2t2: uni > array_int ).
tff(bridgeL2,axiom,
! [I: array_int] : tb2t2(t2tb2(I)) = I ).
tff(bridgeR2,axiom,
! [J: uni] : t2tb2(tb2t2(J)) = J ).
tff(chunk_valid_indexes_def,axiom,
! [Start: array_int,Offsets: array_int] :
( chunk_valid_indexes1(Start,Offsets)
<=> ( ( length1(int,t2tb2(Start)) = 81 )
& ( length1(int,t2tb2(Offsets)) = 9 )
& ! [I: $int,O: $int] :
( ( is_index1(I)
& $lesseq(0,O)
& $less(O,9) )
=> is_index1($sum(tb2t1(get2(int,t2tb2(Start),I)),tb2t1(get2(int,t2tb2(Offsets),O)))) ) ) ) ).
tff(disjoint_chunks,type,
disjoint_chunks1: ( array_int * array_int ) > $o ).
tff(disjoint_chunks_def,axiom,
! [Start: array_int,Offsets: array_int] :
( disjoint_chunks1(Start,Offsets)
<=> ( ( length1(int,t2tb2(Start)) = 81 )
& ( length1(int,t2tb2(Offsets)) = 9 )
& ! [I1: $int,I2: $int,O: $int] :
( ( is_index1(I1)
& is_index1(I2)
& $lesseq(0,O)
& $less(O,9) )
=> ( ( tb2t1(get2(int,t2tb2(Start),I1)) != tb2t1(get2(int,t2tb2(Start),I2)) )
=> ( I1 != $sum(tb2t1(get2(int,t2tb2(Start),I2)),tb2t1(get2(int,t2tb2(Offsets),O))) ) ) ) ) ) ).
tff(well_formed_sudoku,type,
well_formed_sudoku1: sudoku_chunks1 > $o ).
tff(well_formed_sudoku_def,axiom,
! [S: sudoku_chunks1] :
( well_formed_sudoku1(S)
<=> ( chunk_valid_indexes1(column_start1(S),column_offsets1(S))
& chunk_valid_indexes1(row_start1(S),row_offsets1(S))
& chunk_valid_indexes1(square_start1(S),square_offsets1(S))
& disjoint_chunks1(column_start1(S),column_offsets1(S))
& disjoint_chunks1(row_start1(S),row_offsets1(S))
& disjoint_chunks1(square_start1(S),square_offsets1(S)) ) ) ).
tff(valid_chunk,type,
valid_chunk1: ( map_int_int * $int * array_int * array_int ) > $o ).
tff(valid_chunk_def,axiom,
! [G: map_int_int,I: $int,Start: array_int,Offsets: array_int] :
( valid_chunk1(G,I,Start,Offsets)
<=> ! [O1: $int,O2: $int] :
( ( $lesseq(0,O1)
& $less(O1,9)
& $lesseq(0,O2)
& $less(O2,9)
& ( O1 != O2 ) )
=> ( ( $lesseq(1,tb2t1(get(int,int,t2tb(G),t2tb1($sum(tb2t1(get2(int,t2tb2(Start),I)),tb2t1(get2(int,t2tb2(Offsets),O1)))))))
& $lesseq(tb2t1(get(int,int,t2tb(G),t2tb1($sum(tb2t1(get2(int,t2tb2(Start),I)),tb2t1(get2(int,t2tb2(Offsets),O1)))))),9)
& $lesseq(1,tb2t1(get(int,int,t2tb(G),t2tb1($sum(tb2t1(get2(int,t2tb2(Start),I)),tb2t1(get2(int,t2tb2(Offsets),O2)))))))
& $lesseq(tb2t1(get(int,int,t2tb(G),t2tb1($sum(tb2t1(get2(int,t2tb2(Start),I)),tb2t1(get2(int,t2tb2(Offsets),O2)))))),9) )
=> ( tb2t1(get(int,int,t2tb(G),t2tb1($sum(tb2t1(get2(int,t2tb2(Start),I)),tb2t1(get2(int,t2tb2(Offsets),O1)))))) != tb2t1(get(int,int,t2tb(G),t2tb1($sum(tb2t1(get2(int,t2tb2(Start),I)),tb2t1(get2(int,t2tb2(Offsets),O2)))))) ) ) ) ) ).
tff(valid_column,type,
valid_column1: ( sudoku_chunks1 * map_int_int * $int ) > $o ).
tff(valid_column_def,axiom,
! [S: sudoku_chunks1,G: map_int_int,I: $int] :
( valid_column1(S,G,I)
<=> valid_chunk1(G,I,column_start1(S),column_offsets1(S)) ) ).
tff(valid_row,type,
valid_row1: ( sudoku_chunks1 * map_int_int * $int ) > $o ).
tff(valid_row_def,axiom,
! [S: sudoku_chunks1,G: map_int_int,I: $int] :
( valid_row1(S,G,I)
<=> valid_chunk1(G,I,row_start1(S),row_offsets1(S)) ) ).
tff(valid_square,type,
valid_square1: ( sudoku_chunks1 * map_int_int * $int ) > $o ).
tff(valid_square_def,axiom,
! [S: sudoku_chunks1,G: map_int_int,I: $int] :
( valid_square1(S,G,I)
<=> valid_chunk1(G,I,square_start1(S),square_offsets1(S)) ) ).
tff(valid,type,
valid1: ( sudoku_chunks1 * map_int_int ) > $o ).
tff(valid_def,axiom,
! [S: sudoku_chunks1,G: map_int_int] :
( valid1(S,G)
<=> ! [I: $int] :
( is_index1(I)
=> ( valid_column1(S,G,I)
& valid_row1(S,G,I)
& valid_square1(S,G,I) ) ) ) ).
tff(full,type,
full1: map_int_int > $o ).
tff(full_def,axiom,
! [G: map_int_int] :
( full1(G)
<=> ! [I: $int] :
( is_index1(I)
=> ( $lesseq(1,tb2t1(get(int,int,t2tb(G),t2tb1(I))))
& $lesseq(tb2t1(get(int,int,t2tb(G),t2tb1(I))),9) ) ) ) ).
tff(included,type,
included1: ( map_int_int * map_int_int ) > $o ).
tff(included_def,axiom,
! [G1: map_int_int,G2: map_int_int] :
( included1(G1,G2)
<=> ! [I: $int] :
( ( is_index1(I)
& $lesseq(1,tb2t1(get(int,int,t2tb(G1),t2tb1(I))))
& $lesseq(tb2t1(get(int,int,t2tb(G1),t2tb1(I))),9) )
=> ( tb2t1(get(int,int,t2tb(G2),t2tb1(I))) = tb2t1(get(int,int,t2tb(G1),t2tb1(I))) ) ) ) ).
tff(subset_valid_chunk,axiom,
! [G: map_int_int,H: map_int_int] :
( included1(G,H)
=> ! [I: $int,S: array_int,O: array_int] :
( ( is_index1(I)
& chunk_valid_indexes1(S,O)
& valid_chunk1(H,I,S,O) )
=> valid_chunk1(G,I,S,O) ) ) ).
tff(subset_valid,axiom,
! [S: sudoku_chunks1,G: map_int_int,H: map_int_int] :
( ( well_formed_sudoku1(S)
& included1(G,H)
& valid1(S,H) )
=> valid1(S,G) ) ).
tff(is_solution_for,type,
is_solution_for1: ( sudoku_chunks1 * map_int_int * map_int_int ) > $o ).
tff(is_solution_for_def,axiom,
! [S: sudoku_chunks1,Sol: map_int_int,Data: map_int_int] :
( is_solution_for1(S,Sol,Data)
<=> ( included1(Data,Sol)
& full1(Sol)
& valid1(S,Sol) ) ) ).
tff(wP_parameter_classical_sudoku,conjecture,
( $lesseq(0,81)
& ( $lesseq(0,81)
=> ( $lesseq(0,0)
& $less(0,81)
& ! [Cs: map_int_int] :
( ( $lesseq(0,81)
& ( Cs = tb2t(set(int,int,const(int,int,t2tb1(0)),t2tb1(0),t2tb1(0))) ) )
=> ( $lesseq(0,1)
& $less(1,81)
& ! [Cs1: map_int_int] :
( ( $lesseq(0,81)
& ( Cs1 = tb2t(set(int,int,t2tb(Cs),t2tb1(1),t2tb1(1))) ) )
=> ( $lesseq(0,2)
& $less(2,81)
& ! [Cs2: map_int_int] :
( ( $lesseq(0,81)
& ( Cs2 = tb2t(set(int,int,t2tb(Cs1),t2tb1(2),t2tb1(2))) ) )
=> ( $lesseq(0,3)
& $less(3,81)
& ! [Cs3: map_int_int] :
( ( $lesseq(0,81)
& ( Cs3 = tb2t(set(int,int,t2tb(Cs2),t2tb1(3),t2tb1(3))) ) )
=> ( $lesseq(0,4)
& $less(4,81)
& ! [Cs4: map_int_int] :
( ( $lesseq(0,81)
& ( Cs4 = tb2t(set(int,int,t2tb(Cs3),t2tb1(4),t2tb1(4))) ) )
=> ( $lesseq(0,5)
& $less(5,81)
& ! [Cs5: map_int_int] :
( ( $lesseq(0,81)
& ( Cs5 = tb2t(set(int,int,t2tb(Cs4),t2tb1(5),t2tb1(5))) ) )
=> ( $lesseq(0,6)
& $less(6,81)
& ! [Cs6: map_int_int] :
( ( $lesseq(0,81)
& ( Cs6 = tb2t(set(int,int,t2tb(Cs5),t2tb1(6),t2tb1(6))) ) )
=> ( $lesseq(0,7)
& $less(7,81)
& ! [Cs7: map_int_int] :
( ( $lesseq(0,81)
& ( Cs7 = tb2t(set(int,int,t2tb(Cs6),t2tb1(7),t2tb1(7))) ) )
=> ( $lesseq(0,8)
& $less(8,81)
& ! [Cs8: map_int_int] :
( ( $lesseq(0,81)
& ( Cs8 = tb2t(set(int,int,t2tb(Cs7),t2tb1(8),t2tb1(8))) ) )
=> ( $lesseq(0,9)
& $less(9,81)
& ! [Cs9: map_int_int] :
( ( $lesseq(0,81)
& ( Cs9 = tb2t(set(int,int,t2tb(Cs8),t2tb1(9),t2tb1(0))) ) )
=> ( $lesseq(0,10)
& $less(10,81)
& ! [Cs10: map_int_int] :
( ( $lesseq(0,81)
& ( Cs10 = tb2t(set(int,int,t2tb(Cs9),t2tb1(10),t2tb1(1))) ) )
=> ( $lesseq(0,11)
& $less(11,81)
& ! [Cs11: map_int_int] :
( ( $lesseq(0,81)
& ( Cs11 = tb2t(set(int,int,t2tb(Cs10),t2tb1(11),t2tb1(2))) ) )
=> ( $lesseq(0,12)
& $less(12,81)
& ! [Cs12: map_int_int] :
( ( $lesseq(0,81)
& ( Cs12 = tb2t(set(int,int,t2tb(Cs11),t2tb1(12),t2tb1(3))) ) )
=> ( $lesseq(0,13)
& $less(13,81)
& ! [Cs13: map_int_int] :
( ( $lesseq(0,81)
& ( Cs13 = tb2t(set(int,int,t2tb(Cs12),t2tb1(13),t2tb1(4))) ) )
=> ( $lesseq(0,14)
& $less(14,81)
& ! [Cs14: map_int_int] :
( ( $lesseq(0,81)
& ( Cs14 = tb2t(set(int,int,t2tb(Cs13),t2tb1(14),t2tb1(5))) ) )
=> ( $lesseq(0,15)
& $less(15,81)
& ! [Cs15: map_int_int] :
( ( $lesseq(0,81)
& ( Cs15 = tb2t(set(int,int,t2tb(Cs14),t2tb1(15),t2tb1(6))) ) )
=> ( $lesseq(0,16)
& $less(16,81)
& ! [Cs16: map_int_int] :
( ( $lesseq(0,81)
& ( Cs16 = tb2t(set(int,int,t2tb(Cs15),t2tb1(16),t2tb1(7))) ) )
=> ( $lesseq(0,17)
& $less(17,81)
& ! [Cs17: map_int_int] :
( ( $lesseq(0,81)
& ( Cs17 = tb2t(set(int,int,t2tb(Cs16),t2tb1(17),t2tb1(8))) ) )
=> ( $lesseq(0,18)
& $less(18,81)
& ! [Cs18: map_int_int] :
( ( $lesseq(0,81)
& ( Cs18 = tb2t(set(int,int,t2tb(Cs17),t2tb1(18),t2tb1(0))) ) )
=> ( $lesseq(0,19)
& $less(19,81)
& ! [Cs19: map_int_int] :
( ( $lesseq(0,81)
& ( Cs19 = tb2t(set(int,int,t2tb(Cs18),t2tb1(19),t2tb1(1))) ) )
=> ( $lesseq(0,20)
& $less(20,81)
& ! [Cs20: map_int_int] :
( ( $lesseq(0,81)
& ( Cs20 = tb2t(set(int,int,t2tb(Cs19),t2tb1(20),t2tb1(2))) ) )
=> ( $lesseq(0,21)
& $less(21,81)
& ! [Cs21: map_int_int] :
( ( $lesseq(0,81)
& ( Cs21 = tb2t(set(int,int,t2tb(Cs20),t2tb1(21),t2tb1(3))) ) )
=> ( $lesseq(0,22)
& $less(22,81)
& ! [Cs22: map_int_int] :
( ( $lesseq(0,81)
& ( Cs22 = tb2t(set(int,int,t2tb(Cs21),t2tb1(22),t2tb1(4))) ) )
=> ( $lesseq(0,23)
& $less(23,81)
& ! [Cs23: map_int_int] :
( ( $lesseq(0,81)
& ( Cs23 = tb2t(set(int,int,t2tb(Cs22),t2tb1(23),t2tb1(5))) ) )
=> ( $lesseq(0,24)
& $less(24,81)
& ! [Cs24: map_int_int] :
( ( $lesseq(0,81)
& ( Cs24 = tb2t(set(int,int,t2tb(Cs23),t2tb1(24),t2tb1(6))) ) )
=> ( $lesseq(0,25)
& $less(25,81)
& ! [Cs25: map_int_int] :
( ( $lesseq(0,81)
& ( Cs25 = tb2t(set(int,int,t2tb(Cs24),t2tb1(25),t2tb1(7))) ) )
=> ( $lesseq(0,26)
& $less(26,81)
& ! [Cs26: map_int_int] :
( ( $lesseq(0,81)
& ( Cs26 = tb2t(set(int,int,t2tb(Cs25),t2tb1(26),t2tb1(8))) ) )
=> ( $lesseq(0,27)
& $less(27,81)
& ! [Cs27: map_int_int] :
( ( $lesseq(0,81)
& ( Cs27 = tb2t(set(int,int,t2tb(Cs26),t2tb1(27),t2tb1(0))) ) )
=> ( $lesseq(0,28)
& $less(28,81)
& ! [Cs28: map_int_int] :
( ( $lesseq(0,81)
& ( Cs28 = tb2t(set(int,int,t2tb(Cs27),t2tb1(28),t2tb1(1))) ) )
=> ( $lesseq(0,29)
& $less(29,81)
& ! [Cs29: map_int_int] :
( ( $lesseq(0,81)
& ( Cs29 = tb2t(set(int,int,t2tb(Cs28),t2tb1(29),t2tb1(2))) ) )
=> ( $lesseq(0,30)
& $less(30,81)
& ! [Cs30: map_int_int] :
( ( $lesseq(0,81)
& ( Cs30 = tb2t(set(int,int,t2tb(Cs29),t2tb1(30),t2tb1(3))) ) )
=> ( $lesseq(0,31)
& $less(31,81)
& ! [Cs31: map_int_int] :
( ( $lesseq(0,81)
& ( Cs31 = tb2t(set(int,int,t2tb(Cs30),t2tb1(31),t2tb1(4))) ) )
=> ( $lesseq(0,32)
& $less(32,81)
& ! [Cs32: map_int_int] :
( ( $lesseq(0,81)
& ( Cs32 = tb2t(set(int,int,t2tb(Cs31),t2tb1(32),t2tb1(5))) ) )
=> ( $lesseq(0,33)
& $less(33,81)
& ! [Cs33: map_int_int] :
( ( $lesseq(0,81)
& ( Cs33 = tb2t(set(int,int,t2tb(Cs32),t2tb1(33),t2tb1(6))) ) )
=> ( $lesseq(0,34)
& $less(34,81)
& ! [Cs34: map_int_int] :
( ( $lesseq(0,81)
& ( Cs34 = tb2t(set(int,int,t2tb(Cs33),t2tb1(34),t2tb1(7))) ) )
=> ( $lesseq(0,35)
& $less(35,81)
& ! [Cs35: map_int_int] :
( ( $lesseq(0,81)
& ( Cs35 = tb2t(set(int,int,t2tb(Cs34),t2tb1(35),t2tb1(8))) ) )
=> ( $lesseq(0,36)
& $less(36,81)
& ! [Cs36: map_int_int] :
( ( $lesseq(0,81)
& ( Cs36 = tb2t(set(int,int,t2tb(Cs35),t2tb1(36),t2tb1(0))) ) )
=> ( $lesseq(0,37)
& $less(37,81)
& ! [Cs37: map_int_int] :
( ( $lesseq(0,81)
& ( Cs37 = tb2t(set(int,int,t2tb(Cs36),t2tb1(37),t2tb1(1))) ) )
=> ( $lesseq(0,38)
& $less(38,81)
& ! [Cs38: map_int_int] :
( ( $lesseq(0,81)
& ( Cs38 = tb2t(set(int,int,t2tb(Cs37),t2tb1(38),t2tb1(2))) ) )
=> ( $lesseq(0,39)
& $less(39,81)
& ! [Cs39: map_int_int] :
( ( $lesseq(0,81)
& ( Cs39 = tb2t(set(int,int,t2tb(Cs38),t2tb1(39),t2tb1(3))) ) )
=> ( $lesseq(0,40)
& $less(40,81)
& ! [Cs40: map_int_int] :
( ( $lesseq(0,81)
& ( Cs40 = tb2t(set(int,int,t2tb(Cs39),t2tb1(40),t2tb1(4))) ) )
=> ( $lesseq(0,41)
& $less(41,81)
& ! [Cs41: map_int_int] :
( ( $lesseq(0,81)
& ( Cs41 = tb2t(set(int,int,t2tb(Cs40),t2tb1(41),t2tb1(5))) ) )
=> ( $lesseq(0,42)
& $less(42,81)
& ! [Cs42: map_int_int] :
( ( $lesseq(0,81)
& ( Cs42 = tb2t(set(int,int,t2tb(Cs41),t2tb1(42),t2tb1(6))) ) )
=> ( $lesseq(0,43)
& $less(43,81)
& ! [Cs43: map_int_int] :
( ( $lesseq(0,81)
& ( Cs43 = tb2t(set(int,int,t2tb(Cs42),t2tb1(43),t2tb1(7))) ) )
=> ( $lesseq(0,44)
& $less(44,81)
& ! [Cs44: map_int_int] :
( ( $lesseq(0,81)
& ( Cs44 = tb2t(set(int,int,t2tb(Cs43),t2tb1(44),t2tb1(8))) ) )
=> ( $lesseq(0,45)
& $less(45,81)
& ! [Cs45: map_int_int] :
( ( $lesseq(0,81)
& ( Cs45 = tb2t(set(int,int,t2tb(Cs44),t2tb1(45),t2tb1(0))) ) )
=> ( $lesseq(0,46)
& $less(46,81)
& ! [Cs46: map_int_int] :
( ( $lesseq(0,81)
& ( Cs46 = tb2t(set(int,int,t2tb(Cs45),t2tb1(46),t2tb1(1))) ) )
=> ( $lesseq(0,47)
& $less(47,81)
& ! [Cs47: map_int_int] :
( ( $lesseq(0,81)
& ( Cs47 = tb2t(set(int,int,t2tb(Cs46),t2tb1(47),t2tb1(2))) ) )
=> ( $lesseq(0,48)
& $less(48,81)
& ! [Cs48: map_int_int] :
( ( $lesseq(0,81)
& ( Cs48 = tb2t(set(int,int,t2tb(Cs47),t2tb1(48),t2tb1(3))) ) )
=> ( $lesseq(0,49)
& $less(49,81)
& ! [Cs49: map_int_int] :
( ( $lesseq(0,81)
& ( Cs49 = tb2t(set(int,int,t2tb(Cs48),t2tb1(49),t2tb1(4))) ) )
=> ( $lesseq(0,50)
& $less(50,81)
& ! [Cs50: map_int_int] :
( ( $lesseq(0,81)
& ( Cs50 = tb2t(set(int,int,t2tb(Cs49),t2tb1(50),t2tb1(5))) ) )
=> ( $lesseq(0,51)
& $less(51,81)
& ! [Cs51: map_int_int] :
( ( $lesseq(0,81)
& ( Cs51 = tb2t(set(int,int,t2tb(Cs50),t2tb1(51),t2tb1(6))) ) )
=> ( $lesseq(0,52)
& $less(52,81)
& ! [Cs52: map_int_int] :
( ( $lesseq(0,81)
& ( Cs52 = tb2t(set(int,int,t2tb(Cs51),t2tb1(52),t2tb1(7))) ) )
=> ( $lesseq(0,53)
& $less(53,81)
& ! [Cs53: map_int_int] :
( ( $lesseq(0,81)
& ( Cs53 = tb2t(set(int,int,t2tb(Cs52),t2tb1(53),t2tb1(8))) ) )
=> ( $lesseq(0,54)
& $less(54,81)
& ! [Cs54: map_int_int] :
( ( $lesseq(0,81)
& ( Cs54 = tb2t(set(int,int,t2tb(Cs53),t2tb1(54),t2tb1(0))) ) )
=> ( $lesseq(0,55)
& $less(55,81)
& ! [Cs55: map_int_int] :
( ( $lesseq(0,81)
& ( Cs55 = tb2t(set(int,int,t2tb(Cs54),t2tb1(55),t2tb1(1))) ) )
=> ( $lesseq(0,56)
& $less(56,81)
& ! [Cs56: map_int_int] :
( ( $lesseq(0,81)
& ( Cs56 = tb2t(set(int,int,t2tb(Cs55),t2tb1(56),t2tb1(2))) ) )
=> ( $lesseq(0,57)
& $less(57,81)
& ! [Cs57: map_int_int] :
( ( $lesseq(0,81)
& ( Cs57 = tb2t(set(int,int,t2tb(Cs56),t2tb1(57),t2tb1(3))) ) )
=> ( $lesseq(0,58)
& $less(58,81)
& ! [Cs58: map_int_int] :
( ( $lesseq(0,81)
& ( Cs58 = tb2t(set(int,int,t2tb(Cs57),t2tb1(58),t2tb1(4))) ) )
=> ( $lesseq(0,59)
& $less(59,81)
& ! [Cs59: map_int_int] :
( ( $lesseq(0,81)
& ( Cs59 = tb2t(set(int,int,t2tb(Cs58),t2tb1(59),t2tb1(5))) ) )
=> ( $lesseq(0,60)
& $less(60,81)
& ! [Cs60: map_int_int] :
( ( $lesseq(0,81)
& ( Cs60 = tb2t(set(int,int,t2tb(Cs59),t2tb1(60),t2tb1(6))) ) )
=> ( $lesseq(0,61)
& $less(61,81)
& ! [Cs61: map_int_int] :
( ( $lesseq(0,81)
& ( Cs61 = tb2t(set(int,int,t2tb(Cs60),t2tb1(61),t2tb1(7))) ) )
=> ( $lesseq(0,62)
& $less(62,81)
& ! [Cs62: map_int_int] :
( ( $lesseq(0,81)
& ( Cs62 = tb2t(set(int,int,t2tb(Cs61),t2tb1(62),t2tb1(8))) ) )
=> ( $lesseq(0,63)
& $less(63,81)
& ! [Cs63: map_int_int] :
( ( $lesseq(0,81)
& ( Cs63 = tb2t(set(int,int,t2tb(Cs62),t2tb1(63),t2tb1(0))) ) )
=> ( $lesseq(0,64)
& $less(64,81)
& ! [Cs64: map_int_int] :
( ( $lesseq(0,81)
& ( Cs64 = tb2t(set(int,int,t2tb(Cs63),t2tb1(64),t2tb1(1))) ) )
=> ( $lesseq(0,65)
& $less(65,81)
& ! [Cs65: map_int_int] :
( ( $lesseq(0,81)
& ( Cs65 = tb2t(set(int,int,t2tb(Cs64),t2tb1(65),t2tb1(2))) ) )
=> ( $lesseq(0,66)
& $less(66,81)
& ! [Cs66: map_int_int] :
( ( $lesseq(0,81)
& ( Cs66 = tb2t(set(int,int,t2tb(Cs65),t2tb1(66),t2tb1(3))) ) )
=> ( $lesseq(0,67)
& $less(67,81)
& ! [Cs67: map_int_int] :
( ( $lesseq(0,81)
& ( Cs67 = tb2t(set(int,int,t2tb(Cs66),t2tb1(67),t2tb1(4))) ) )
=> ( $lesseq(0,68)
& $less(68,81)
& ! [Cs68: map_int_int] :
( ( $lesseq(0,81)
& ( Cs68 = tb2t(set(int,int,t2tb(Cs67),t2tb1(68),t2tb1(5))) ) )
=> ( $lesseq(0,69)
& $less(69,81)
& ! [Cs69: map_int_int] :
( ( $lesseq(0,81)
& ( Cs69 = tb2t(set(int,int,t2tb(Cs68),t2tb1(69),t2tb1(6))) ) )
=> ( $lesseq(0,70)
& $less(70,81)
& ! [Cs70: map_int_int] :
( ( $lesseq(0,81)
& ( Cs70 = tb2t(set(int,int,t2tb(Cs69),t2tb1(70),t2tb1(7))) ) )
=> ( $lesseq(0,71)
& $less(71,81)
& ! [Cs71: map_int_int] :
( ( $lesseq(0,81)
& ( Cs71 = tb2t(set(int,int,t2tb(Cs70),t2tb1(71),t2tb1(8))) ) )
=> ( $lesseq(0,72)
& $less(72,81)
& ! [Cs72: map_int_int] :
( ( $lesseq(0,81)
& ( Cs72 = tb2t(set(int,int,t2tb(Cs71),t2tb1(72),t2tb1(0))) ) )
=> ( $lesseq(0,73)
& $less(73,81)
& ! [Cs73: map_int_int] :
( ( $lesseq(0,81)
& ( Cs73 = tb2t(set(int,int,t2tb(Cs72),t2tb1(73),t2tb1(1))) ) )
=> ( $lesseq(0,74)
& $less(74,81)
& ! [Cs74: map_int_int] :
( ( $lesseq(0,81)
& ( Cs74 = tb2t(set(int,int,t2tb(Cs73),t2tb1(74),t2tb1(2))) ) )
=> ( $lesseq(0,75)
& $less(75,81)
& ! [Cs75: map_int_int] :
( ( $lesseq(0,81)
& ( Cs75 = tb2t(set(int,int,t2tb(Cs74),t2tb1(75),t2tb1(3))) ) )
=> ( $lesseq(0,76)
& $less(76,81)
& ! [Cs76: map_int_int] :
( ( $lesseq(0,81)
& ( Cs76 = tb2t(set(int,int,t2tb(Cs75),t2tb1(76),t2tb1(4))) ) )
=> ( $lesseq(0,77)
& $less(77,81)
& ! [Cs77: map_int_int] :
( ( $lesseq(0,81)
& ( Cs77 = tb2t(set(int,int,t2tb(Cs76),t2tb1(77),t2tb1(5))) ) )
=> ( $lesseq(0,78)
& $less(78,81)
& ! [Cs78: map_int_int] :
( ( $lesseq(0,81)
& ( Cs78 = tb2t(set(int,int,t2tb(Cs77),t2tb1(78),t2tb1(6))) ) )
=> ( $lesseq(0,79)
& $less(79,81)
& ! [Cs79: map_int_int] :
( ( $lesseq(0,81)
& ( Cs79 = tb2t(set(int,int,t2tb(Cs78),t2tb1(79),t2tb1(7))) ) )
=> ( $lesseq(0,80)
& $less(80,81)
& ! [Cs80: map_int_int] :
( ( $lesseq(0,81)
& ( Cs80 = tb2t(set(int,int,t2tb(Cs79),t2tb1(80),t2tb1(8))) ) )
=> ( $lesseq(0,9)
& ( $lesseq(0,9)
=> ( $lesseq(0,0)
& $less(0,9)
& ! [Co: map_int_int] :
( ( $lesseq(0,9)
& ( Co = tb2t(set(int,int,const(int,int,t2tb1(0)),t2tb1(0),t2tb1(0))) ) )
=> ( $lesseq(0,1)
& $less(1,9)
& ! [Co1: map_int_int] :
( ( $lesseq(0,9)
& ( Co1 = tb2t(set(int,int,t2tb(Co),t2tb1(1),t2tb1(9))) ) )
=> ( $lesseq(0,2)
& $less(2,9)
& ! [Co2: map_int_int] :
( ( $lesseq(0,9)
& ( Co2 = tb2t(set(int,int,t2tb(Co1),t2tb1(2),t2tb1(18))) ) )
=> ( $lesseq(0,3)
& $less(3,9)
& ! [Co3: map_int_int] :
( ( $lesseq(0,9)
& ( Co3 = tb2t(set(int,int,t2tb(Co2),t2tb1(3),t2tb1(27))) ) )
=> ( $lesseq(0,4)
& $less(4,9)
& ! [Co4: map_int_int] :
( ( $lesseq(0,9)
& ( Co4 = tb2t(set(int,int,t2tb(Co3),t2tb1(4),t2tb1(36))) ) )
=> ( $lesseq(0,5)
& $less(5,9)
& ! [Co5: map_int_int] :
( ( $lesseq(0,9)
& ( Co5 = tb2t(set(int,int,t2tb(Co4),t2tb1(5),t2tb1(45))) ) )
=> ( $lesseq(0,6)
& $less(6,9)
& ! [Co6: map_int_int] :
( ( $lesseq(0,9)
& ( Co6 = tb2t(set(int,int,t2tb(Co5),t2tb1(6),t2tb1(54))) ) )
=> ( $lesseq(0,7)
& $less(7,9)
& ! [Co7: map_int_int] :
( ( $lesseq(0,9)
& ( Co7 = tb2t(set(int,int,t2tb(Co6),t2tb1(7),t2tb1(63))) ) )
=> ( $lesseq(0,8)
& $less(8,9)
& ! [Co8: map_int_int] :
( ( $lesseq(0,9)
& ( Co8 = tb2t(set(int,int,t2tb(Co7),t2tb1(8),t2tb1(72))) ) )
=> ( $lesseq(0,81)
& ( $lesseq(0,81)
=> ( $lesseq(0,0)
& $less(0,81)
& ! [Rs: map_int_int] :
( ( $lesseq(0,81)
& ( Rs = tb2t(set(int,int,const(int,int,t2tb1(0)),t2tb1(0),t2tb1(0))) ) )
=> ( $lesseq(0,1)
& $less(1,81)
& ! [Rs1: map_int_int] :
( ( $lesseq(0,81)
& ( Rs1 = tb2t(set(int,int,t2tb(Rs),t2tb1(1),t2tb1(0))) ) )
=> ( $lesseq(0,2)
& $less(2,81)
& ! [Rs2: map_int_int] :
( ( $lesseq(0,81)
& ( Rs2 = tb2t(set(int,int,t2tb(Rs1),t2tb1(2),t2tb1(0))) ) )
=> ( $lesseq(0,3)
& $less(3,81)
& ! [Rs3: map_int_int] :
( ( $lesseq(0,81)
& ( Rs3 = tb2t(set(int,int,t2tb(Rs2),t2tb1(3),t2tb1(0))) ) )
=> ( $lesseq(0,4)
& $less(4,81)
& ! [Rs4: map_int_int] :
( ( $lesseq(0,81)
& ( Rs4 = tb2t(set(int,int,t2tb(Rs3),t2tb1(4),t2tb1(0))) ) )
=> ( $lesseq(0,5)
& $less(5,81)
& ! [Rs5: map_int_int] :
( ( $lesseq(0,81)
& ( Rs5 = tb2t(set(int,int,t2tb(Rs4),t2tb1(5),t2tb1(0))) ) )
=> ( $lesseq(0,6)
& $less(6,81)
& ! [Rs6: map_int_int] :
( ( $lesseq(0,81)
& ( Rs6 = tb2t(set(int,int,t2tb(Rs5),t2tb1(6),t2tb1(0))) ) )
=> ( $lesseq(0,7)
& $less(7,81)
& ! [Rs7: map_int_int] :
( ( $lesseq(0,81)
& ( Rs7 = tb2t(set(int,int,t2tb(Rs6),t2tb1(7),t2tb1(0))) ) )
=> ( $lesseq(0,8)
& $less(8,81)
& ! [Rs8: map_int_int] :
( ( $lesseq(0,81)
& ( Rs8 = tb2t(set(int,int,t2tb(Rs7),t2tb1(8),t2tb1(0))) ) )
=> ( $lesseq(0,9)
& $less(9,81)
& ! [Rs9: map_int_int] :
( ( $lesseq(0,81)
& ( Rs9 = tb2t(set(int,int,t2tb(Rs8),t2tb1(9),t2tb1(9))) ) )
=> ( $lesseq(0,10)
& $less(10,81)
& ! [Rs10: map_int_int] :
( ( $lesseq(0,81)
& ( Rs10 = tb2t(set(int,int,t2tb(Rs9),t2tb1(10),t2tb1(9))) ) )
=> ( $lesseq(0,11)
& $less(11,81)
& ! [Rs11: map_int_int] :
( ( $lesseq(0,81)
& ( Rs11 = tb2t(set(int,int,t2tb(Rs10),t2tb1(11),t2tb1(9))) ) )
=> ( $lesseq(0,12)
& $less(12,81)
& ! [Rs12: map_int_int] :
( ( $lesseq(0,81)
& ( Rs12 = tb2t(set(int,int,t2tb(Rs11),t2tb1(12),t2tb1(9))) ) )
=> ( $lesseq(0,13)
& $less(13,81)
& ! [Rs13: map_int_int] :
( ( $lesseq(0,81)
& ( Rs13 = tb2t(set(int,int,t2tb(Rs12),t2tb1(13),t2tb1(9))) ) )
=> ( $lesseq(0,14)
& $less(14,81)
& ! [Rs14: map_int_int] :
( ( $lesseq(0,81)
& ( Rs14 = tb2t(set(int,int,t2tb(Rs13),t2tb1(14),t2tb1(9))) ) )
=> ( $lesseq(0,15)
& $less(15,81)
& ! [Rs15: map_int_int] :
( ( $lesseq(0,81)
& ( Rs15 = tb2t(set(int,int,t2tb(Rs14),t2tb1(15),t2tb1(9))) ) )
=> ( $lesseq(0,16)
& $less(16,81)
& ! [Rs16: map_int_int] :
( ( $lesseq(0,81)
& ( Rs16 = tb2t(set(int,int,t2tb(Rs15),t2tb1(16),t2tb1(9))) ) )
=> ( $lesseq(0,17)
& $less(17,81)
& ! [Rs17: map_int_int] :
( ( $lesseq(0,81)
& ( Rs17 = tb2t(set(int,int,t2tb(Rs16),t2tb1(17),t2tb1(9))) ) )
=> ( $lesseq(0,18)
& $less(18,81)
& ! [Rs18: map_int_int] :
( ( $lesseq(0,81)
& ( Rs18 = tb2t(set(int,int,t2tb(Rs17),t2tb1(18),t2tb1(18))) ) )
=> ( $lesseq(0,19)
& $less(19,81)
& ! [Rs19: map_int_int] :
( ( $lesseq(0,81)
& ( Rs19 = tb2t(set(int,int,t2tb(Rs18),t2tb1(19),t2tb1(18))) ) )
=> ( $lesseq(0,20)
& $less(20,81)
& ! [Rs20: map_int_int] :
( ( $lesseq(0,81)
& ( Rs20 = tb2t(set(int,int,t2tb(Rs19),t2tb1(20),t2tb1(18))) ) )
=> ( $lesseq(0,21)
& $less(21,81)
& ! [Rs21: map_int_int] :
( ( $lesseq(0,81)
& ( Rs21 = tb2t(set(int,int,t2tb(Rs20),t2tb1(21),t2tb1(18))) ) )
=> ( $lesseq(0,22)
& $less(22,81)
& ! [Rs22: map_int_int] :
( ( $lesseq(0,81)
& ( Rs22 = tb2t(set(int,int,t2tb(Rs21),t2tb1(22),t2tb1(18))) ) )
=> ( $lesseq(0,23)
& $less(23,81)
& ! [Rs23: map_int_int] :
( ( $lesseq(0,81)
& ( Rs23 = tb2t(set(int,int,t2tb(Rs22),t2tb1(23),t2tb1(18))) ) )
=> ( $lesseq(0,24)
& $less(24,81)
& ! [Rs24: map_int_int] :
( ( $lesseq(0,81)
& ( Rs24 = tb2t(set(int,int,t2tb(Rs23),t2tb1(24),t2tb1(18))) ) )
=> ( $lesseq(0,25)
& $less(25,81)
& ! [Rs25: map_int_int] :
( ( $lesseq(0,81)
& ( Rs25 = tb2t(set(int,int,t2tb(Rs24),t2tb1(25),t2tb1(18))) ) )
=> ( $lesseq(0,26)
& $less(26,81)
& ! [Rs26: map_int_int] :
( ( $lesseq(0,81)
& ( Rs26 = tb2t(set(int,int,t2tb(Rs25),t2tb1(26),t2tb1(18))) ) )
=> ( $lesseq(0,27)
& $less(27,81)
& ! [Rs27: map_int_int] :
( ( $lesseq(0,81)
& ( Rs27 = tb2t(set(int,int,t2tb(Rs26),t2tb1(27),t2tb1(27))) ) )
=> ( $lesseq(0,28)
& $less(28,81)
& ! [Rs28: map_int_int] :
( ( $lesseq(0,81)
& ( Rs28 = tb2t(set(int,int,t2tb(Rs27),t2tb1(28),t2tb1(27))) ) )
=> ( $lesseq(0,29)
& $less(29,81)
& ! [Rs29: map_int_int] :
( ( $lesseq(0,81)
& ( Rs29 = tb2t(set(int,int,t2tb(Rs28),t2tb1(29),t2tb1(27))) ) )
=> ( $lesseq(0,30)
& $less(30,81)
& ! [Rs30: map_int_int] :
( ( $lesseq(0,81)
& ( Rs30 = tb2t(set(int,int,t2tb(Rs29),t2tb1(30),t2tb1(27))) ) )
=> ( $lesseq(0,31)
& $less(31,81)
& ! [Rs31: map_int_int] :
( ( $lesseq(0,81)
& ( Rs31 = tb2t(set(int,int,t2tb(Rs30),t2tb1(31),t2tb1(27))) ) )
=> ( $lesseq(0,32)
& $less(32,81)
& ! [Rs32: map_int_int] :
( ( $lesseq(0,81)
& ( Rs32 = tb2t(set(int,int,t2tb(Rs31),t2tb1(32),t2tb1(27))) ) )
=> ( $lesseq(0,33)
& $less(33,81)
& ! [Rs33: map_int_int] :
( ( $lesseq(0,81)
& ( Rs33 = tb2t(set(int,int,t2tb(Rs32),t2tb1(33),t2tb1(27))) ) )
=> ( $lesseq(0,34)
& $less(34,81)
& ! [Rs34: map_int_int] :
( ( $lesseq(0,81)
& ( Rs34 = tb2t(set(int,int,t2tb(Rs33),t2tb1(34),t2tb1(27))) ) )
=> ( $lesseq(0,35)
& $less(35,81)
& ! [Rs35: map_int_int] :
( ( $lesseq(0,81)
& ( Rs35 = tb2t(set(int,int,t2tb(Rs34),t2tb1(35),t2tb1(27))) ) )
=> ( $lesseq(0,36)
& $less(36,81)
& ! [Rs36: map_int_int] :
( ( $lesseq(0,81)
& ( Rs36 = tb2t(set(int,int,t2tb(Rs35),t2tb1(36),t2tb1(36))) ) )
=> ( $lesseq(0,37)
& $less(37,81)
& ! [Rs37: map_int_int] :
( ( $lesseq(0,81)
& ( Rs37 = tb2t(set(int,int,t2tb(Rs36),t2tb1(37),t2tb1(36))) ) )
=> ( $lesseq(0,38)
& $less(38,81)
& ! [Rs38: map_int_int] :
( ( $lesseq(0,81)
& ( Rs38 = tb2t(set(int,int,t2tb(Rs37),t2tb1(38),t2tb1(36))) ) )
=> ( $lesseq(0,39)
& $less(39,81)
& ! [Rs39: map_int_int] :
( ( $lesseq(0,81)
& ( Rs39 = tb2t(set(int,int,t2tb(Rs38),t2tb1(39),t2tb1(36))) ) )
=> ( $lesseq(0,40)
& $less(40,81)
& ! [Rs40: map_int_int] :
( ( $lesseq(0,81)
& ( Rs40 = tb2t(set(int,int,t2tb(Rs39),t2tb1(40),t2tb1(36))) ) )
=> ( $lesseq(0,41)
& $less(41,81)
& ! [Rs41: map_int_int] :
( ( $lesseq(0,81)
& ( Rs41 = tb2t(set(int,int,t2tb(Rs40),t2tb1(41),t2tb1(36))) ) )
=> ( $lesseq(0,42)
& $less(42,81)
& ! [Rs42: map_int_int] :
( ( $lesseq(0,81)
& ( Rs42 = tb2t(set(int,int,t2tb(Rs41),t2tb1(42),t2tb1(36))) ) )
=> ( $lesseq(0,43)
& $less(43,81)
& ! [Rs43: map_int_int] :
( ( $lesseq(0,81)
& ( Rs43 = tb2t(set(int,int,t2tb(Rs42),t2tb1(43),t2tb1(36))) ) )
=> ( $lesseq(0,44)
& $less(44,81)
& ! [Rs44: map_int_int] :
( ( $lesseq(0,81)
& ( Rs44 = tb2t(set(int,int,t2tb(Rs43),t2tb1(44),t2tb1(36))) ) )
=> ( $lesseq(0,45)
& $less(45,81)
& ! [Rs45: map_int_int] :
( ( $lesseq(0,81)
& ( Rs45 = tb2t(set(int,int,t2tb(Rs44),t2tb1(45),t2tb1(45))) ) )
=> ( $lesseq(0,46)
& $less(46,81)
& ! [Rs46: map_int_int] :
( ( $lesseq(0,81)
& ( Rs46 = tb2t(set(int,int,t2tb(Rs45),t2tb1(46),t2tb1(45))) ) )
=> ( $lesseq(0,47)
& $less(47,81)
& ! [Rs47: map_int_int] :
( ( $lesseq(0,81)
& ( Rs47 = tb2t(set(int,int,t2tb(Rs46),t2tb1(47),t2tb1(45))) ) )
=> ( $lesseq(0,48)
& $less(48,81)
& ! [Rs48: map_int_int] :
( ( $lesseq(0,81)
& ( Rs48 = tb2t(set(int,int,t2tb(Rs47),t2tb1(48),t2tb1(45))) ) )
=> ( $lesseq(0,49)
& $less(49,81)
& ! [Rs49: map_int_int] :
( ( $lesseq(0,81)
& ( Rs49 = tb2t(set(int,int,t2tb(Rs48),t2tb1(49),t2tb1(45))) ) )
=> ( $lesseq(0,50)
& $less(50,81)
& ! [Rs50: map_int_int] :
( ( $lesseq(0,81)
& ( Rs50 = tb2t(set(int,int,t2tb(Rs49),t2tb1(50),t2tb1(45))) ) )
=> ( $lesseq(0,51)
& $less(51,81)
& ! [Rs51: map_int_int] :
( ( $lesseq(0,81)
& ( Rs51 = tb2t(set(int,int,t2tb(Rs50),t2tb1(51),t2tb1(45))) ) )
=> ( $lesseq(0,52)
& $less(52,81)
& ! [Rs52: map_int_int] :
( ( $lesseq(0,81)
& ( Rs52 = tb2t(set(int,int,t2tb(Rs51),t2tb1(52),t2tb1(45))) ) )
=> ( $lesseq(0,53)
& $less(53,81)
& ! [Rs53: map_int_int] :
( ( $lesseq(0,81)
& ( Rs53 = tb2t(set(int,int,t2tb(Rs52),t2tb1(53),t2tb1(45))) ) )
=> ( $lesseq(0,54)
& $less(54,81)
& ! [Rs54: map_int_int] :
( ( $lesseq(0,81)
& ( Rs54 = tb2t(set(int,int,t2tb(Rs53),t2tb1(54),t2tb1(54))) ) )
=> ( $lesseq(0,55)
& $less(55,81)
& ! [Rs55: map_int_int] :
( ( $lesseq(0,81)
& ( Rs55 = tb2t(set(int,int,t2tb(Rs54),t2tb1(55),t2tb1(54))) ) )
=> ( $lesseq(0,56)
& $less(56,81)
& ! [Rs56: map_int_int] :
( ( $lesseq(0,81)
& ( Rs56 = tb2t(set(int,int,t2tb(Rs55),t2tb1(56),t2tb1(54))) ) )
=> ( $lesseq(0,57)
& $less(57,81)
& ! [Rs57: map_int_int] :
( ( $lesseq(0,81)
& ( Rs57 = tb2t(set(int,int,t2tb(Rs56),t2tb1(57),t2tb1(54))) ) )
=> ( $lesseq(0,58)
& $less(58,81)
& ! [Rs58: map_int_int] :
( ( $lesseq(0,81)
& ( Rs58 = tb2t(set(int,int,t2tb(Rs57),t2tb1(58),t2tb1(54))) ) )
=> ( $lesseq(0,59)
& $less(59,81)
& ! [Rs59: map_int_int] :
( ( $lesseq(0,81)
& ( Rs59 = tb2t(set(int,int,t2tb(Rs58),t2tb1(59),t2tb1(54))) ) )
=> ( $lesseq(0,60)
& $less(60,81)
& ! [Rs60: map_int_int] :
( ( $lesseq(0,81)
& ( Rs60 = tb2t(set(int,int,t2tb(Rs59),t2tb1(60),t2tb1(54))) ) )
=> ( $lesseq(0,61)
& $less(61,81)
& ! [Rs61: map_int_int] :
( ( $lesseq(0,81)
& ( Rs61 = tb2t(set(int,int,t2tb(Rs60),t2tb1(61),t2tb1(54))) ) )
=> ( $lesseq(0,62)
& $less(62,81)
& ! [Rs62: map_int_int] :
( ( $lesseq(0,81)
& ( Rs62 = tb2t(set(int,int,t2tb(Rs61),t2tb1(62),t2tb1(54))) ) )
=> ( $lesseq(0,63)
& $less(63,81)
& ! [Rs63: map_int_int] :
( ( $lesseq(0,81)
& ( Rs63 = tb2t(set(int,int,t2tb(Rs62),t2tb1(63),t2tb1(63))) ) )
=> ( $lesseq(0,64)
& $less(64,81)
& ! [Rs64: map_int_int] :
( ( $lesseq(0,81)
& ( Rs64 = tb2t(set(int,int,t2tb(Rs63),t2tb1(64),t2tb1(63))) ) )
=> ( $lesseq(0,65)
& $less(65,81)
& ! [Rs65: map_int_int] :
( ( $lesseq(0,81)
& ( Rs65 = tb2t(set(int,int,t2tb(Rs64),t2tb1(65),t2tb1(63))) ) )
=> ( $lesseq(0,66)
& $less(66,81)
& ! [Rs66: map_int_int] :
( ( $lesseq(0,81)
& ( Rs66 = tb2t(set(int,int,t2tb(Rs65),t2tb1(66),t2tb1(63))) ) )
=> ( $lesseq(0,67)
& $less(67,81)
& ! [Rs67: map_int_int] :
( ( $lesseq(0,81)
& ( Rs67 = tb2t(set(int,int,t2tb(Rs66),t2tb1(67),t2tb1(63))) ) )
=> ( $lesseq(0,68)
& $less(68,81)
& ! [Rs68: map_int_int] :
( ( $lesseq(0,81)
& ( Rs68 = tb2t(set(int,int,t2tb(Rs67),t2tb1(68),t2tb1(63))) ) )
=> ( $lesseq(0,69)
& $less(69,81)
& ! [Rs69: map_int_int] :
( ( $lesseq(0,81)
& ( Rs69 = tb2t(set(int,int,t2tb(Rs68),t2tb1(69),t2tb1(63))) ) )
=> ( $lesseq(0,70)
& $less(70,81)
& ! [Rs70: map_int_int] :
( ( $lesseq(0,81)
& ( Rs70 = tb2t(set(int,int,t2tb(Rs69),t2tb1(70),t2tb1(63))) ) )
=> ( $lesseq(0,71)
& $less(71,81)
& ! [Rs71: map_int_int] :
( ( $lesseq(0,81)
& ( Rs71 = tb2t(set(int,int,t2tb(Rs70),t2tb1(71),t2tb1(63))) ) )
=> ( $lesseq(0,72)
& $less(72,81)
& ! [Rs72: map_int_int] :
( ( $lesseq(0,81)
& ( Rs72 = tb2t(set(int,int,t2tb(Rs71),t2tb1(72),t2tb1(72))) ) )
=> ( $lesseq(0,73)
& $less(73,81)
& ! [Rs73: map_int_int] :
( ( $lesseq(0,81)
& ( Rs73 = tb2t(set(int,int,t2tb(Rs72),t2tb1(73),t2tb1(72))) ) )
=> ( $lesseq(0,74)
& $less(74,81)
& ! [Rs74: map_int_int] :
( ( $lesseq(0,81)
& ( Rs74 = tb2t(set(int,int,t2tb(Rs73),t2tb1(74),t2tb1(72))) ) )
=> ( $lesseq(0,75)
& $less(75,81)
& ! [Rs75: map_int_int] :
( ( $lesseq(0,81)
& ( Rs75 = tb2t(set(int,int,t2tb(Rs74),t2tb1(75),t2tb1(72))) ) )
=> ( $lesseq(0,76)
& $less(76,81)
& ! [Rs76: map_int_int] :
( ( $lesseq(0,81)
& ( Rs76 = tb2t(set(int,int,t2tb(Rs75),t2tb1(76),t2tb1(72))) ) )
=> ( $lesseq(0,77)
& $less(77,81)
& ! [Rs77: map_int_int] :
( ( $lesseq(0,81)
& ( Rs77 = tb2t(set(int,int,t2tb(Rs76),t2tb1(77),t2tb1(72))) ) )
=> ( $lesseq(0,78)
& $less(78,81)
& ! [Rs78: map_int_int] :
( ( $lesseq(0,81)
& ( Rs78 = tb2t(set(int,int,t2tb(Rs77),t2tb1(78),t2tb1(72))) ) )
=> ( $lesseq(0,79)
& $less(79,81)
& ! [Rs79: map_int_int] :
( ( $lesseq(0,81)
& ( Rs79 = tb2t(set(int,int,t2tb(Rs78),t2tb1(79),t2tb1(72))) ) )
=> ( $lesseq(0,80)
& $less(80,81)
& ! [Rs80: map_int_int] :
( ( $lesseq(0,81)
& ( Rs80 = tb2t(set(int,int,t2tb(Rs79),t2tb1(80),t2tb1(72))) ) )
=> ( $lesseq(0,9)
& ( $lesseq(0,9)
=> ( $lesseq(0,0)
& $less(0,9)
& ! [Ro: map_int_int] :
( ( $lesseq(0,9)
& ( Ro = tb2t(set(int,int,const(int,int,t2tb1(0)),t2tb1(0),t2tb1(0))) ) )
=> ( $lesseq(0,1)
& $less(1,9)
& ! [Ro1: map_int_int] :
( ( $lesseq(0,9)
& ( Ro1 = tb2t(set(int,int,t2tb(Ro),t2tb1(1),t2tb1(1))) ) )
=> ( $lesseq(0,2)
& $less(2,9)
& ! [Ro2: map_int_int] :
( ( $lesseq(0,9)
& ( Ro2 = tb2t(set(int,int,t2tb(Ro1),t2tb1(2),t2tb1(2))) ) )
=> ( $lesseq(0,3)
& $less(3,9)
& ! [Ro3: map_int_int] :
( ( $lesseq(0,9)
& ( Ro3 = tb2t(set(int,int,t2tb(Ro2),t2tb1(3),t2tb1(3))) ) )
=> ( $lesseq(0,4)
& $less(4,9)
& ! [Ro4: map_int_int] :
( ( $lesseq(0,9)
& ( Ro4 = tb2t(set(int,int,t2tb(Ro3),t2tb1(4),t2tb1(4))) ) )
=> ( $lesseq(0,5)
& $less(5,9)
& ! [Ro5: map_int_int] :
( ( $lesseq(0,9)
& ( Ro5 = tb2t(set(int,int,t2tb(Ro4),t2tb1(5),t2tb1(5))) ) )
=> ( $lesseq(0,6)
& $less(6,9)
& ! [Ro6: map_int_int] :
( ( $lesseq(0,9)
& ( Ro6 = tb2t(set(int,int,t2tb(Ro5),t2tb1(6),t2tb1(6))) ) )
=> ( $lesseq(0,7)
& $less(7,9)
& ! [Ro7: map_int_int] :
( ( $lesseq(0,9)
& ( Ro7 = tb2t(set(int,int,t2tb(Ro6),t2tb1(7),t2tb1(7))) ) )
=> ( $lesseq(0,8)
& $less(8,9)
& ! [Ro8: map_int_int] :
( ( $lesseq(0,9)
& ( Ro8 = tb2t(set(int,int,t2tb(Ro7),t2tb1(8),t2tb1(8))) ) )
=> ( $lesseq(0,81)
& ( $lesseq(0,81)
=> ( $lesseq(0,0)
& $less(0,81)
& ! [Ss: map_int_int] :
( ( $lesseq(0,81)
& ( Ss = tb2t(set(int,int,const(int,int,t2tb1(0)),t2tb1(0),t2tb1(0))) ) )
=> ( $lesseq(0,1)
& $less(1,81)
& ! [Ss1: map_int_int] :
( ( $lesseq(0,81)
& ( Ss1 = tb2t(set(int,int,t2tb(Ss),t2tb1(1),t2tb1(0))) ) )
=> ( $lesseq(0,2)
& $less(2,81)
& ! [Ss2: map_int_int] :
( ( $lesseq(0,81)
& ( Ss2 = tb2t(set(int,int,t2tb(Ss1),t2tb1(2),t2tb1(0))) ) )
=> ( $lesseq(0,3)
& $less(3,81)
& ! [Ss3: map_int_int] :
( ( $lesseq(0,81)
& ( Ss3 = tb2t(set(int,int,t2tb(Ss2),t2tb1(3),t2tb1(3))) ) )
=> ( $lesseq(0,4)
& $less(4,81)
& ! [Ss4: map_int_int] :
( ( $lesseq(0,81)
& ( Ss4 = tb2t(set(int,int,t2tb(Ss3),t2tb1(4),t2tb1(3))) ) )
=> ( $lesseq(0,5)
& $less(5,81)
& ! [Ss5: map_int_int] :
( ( $lesseq(0,81)
& ( Ss5 = tb2t(set(int,int,t2tb(Ss4),t2tb1(5),t2tb1(3))) ) )
=> ( $lesseq(0,6)
& $less(6,81)
& ! [Ss6: map_int_int] :
( ( $lesseq(0,81)
& ( Ss6 = tb2t(set(int,int,t2tb(Ss5),t2tb1(6),t2tb1(6))) ) )
=> ( $lesseq(0,7)
& $less(7,81)
& ! [Ss7: map_int_int] :
( ( $lesseq(0,81)
& ( Ss7 = tb2t(set(int,int,t2tb(Ss6),t2tb1(7),t2tb1(6))) ) )
=> ( $lesseq(0,8)
& $less(8,81)
& ! [Ss8: map_int_int] :
( ( $lesseq(0,81)
& ( Ss8 = tb2t(set(int,int,t2tb(Ss7),t2tb1(8),t2tb1(6))) ) )
=> ( $lesseq(0,9)
& $less(9,81)
& ! [Ss9: map_int_int] :
( ( $lesseq(0,81)
& ( Ss9 = tb2t(set(int,int,t2tb(Ss8),t2tb1(9),t2tb1(0))) ) )
=> ( $lesseq(0,10)
& $less(10,81)
& ! [Ss10: map_int_int] :
( ( $lesseq(0,81)
& ( Ss10 = tb2t(set(int,int,t2tb(Ss9),t2tb1(10),t2tb1(0))) ) )
=> ( $lesseq(0,11)
& $less(11,81)
& ! [Ss11: map_int_int] :
( ( $lesseq(0,81)
& ( Ss11 = tb2t(set(int,int,t2tb(Ss10),t2tb1(11),t2tb1(0))) ) )
=> ( $lesseq(0,12)
& $less(12,81)
& ! [Ss12: map_int_int] :
( ( $lesseq(0,81)
& ( Ss12 = tb2t(set(int,int,t2tb(Ss11),t2tb1(12),t2tb1(3))) ) )
=> ( $lesseq(0,13)
& $less(13,81)
& ! [Ss13: map_int_int] :
( ( $lesseq(0,81)
& ( Ss13 = tb2t(set(int,int,t2tb(Ss12),t2tb1(13),t2tb1(3))) ) )
=> ( $lesseq(0,14)
& $less(14,81)
& ! [Ss14: map_int_int] :
( ( $lesseq(0,81)
& ( Ss14 = tb2t(set(int,int,t2tb(Ss13),t2tb1(14),t2tb1(3))) ) )
=> ( $lesseq(0,15)
& $less(15,81)
& ! [Ss15: map_int_int] :
( ( $lesseq(0,81)
& ( Ss15 = tb2t(set(int,int,t2tb(Ss14),t2tb1(15),t2tb1(6))) ) )
=> ( $lesseq(0,16)
& $less(16,81)
& ! [Ss16: map_int_int] :
( ( $lesseq(0,81)
& ( Ss16 = tb2t(set(int,int,t2tb(Ss15),t2tb1(16),t2tb1(6))) ) )
=> ( $lesseq(0,17)
& $less(17,81)
& ! [Ss17: map_int_int] :
( ( $lesseq(0,81)
& ( Ss17 = tb2t(set(int,int,t2tb(Ss16),t2tb1(17),t2tb1(6))) ) )
=> ( $lesseq(0,18)
& $less(18,81)
& ! [Ss18: map_int_int] :
( ( $lesseq(0,81)
& ( Ss18 = tb2t(set(int,int,t2tb(Ss17),t2tb1(18),t2tb1(0))) ) )
=> ( $lesseq(0,19)
& $less(19,81)
& ! [Ss19: map_int_int] :
( ( $lesseq(0,81)
& ( Ss19 = tb2t(set(int,int,t2tb(Ss18),t2tb1(19),t2tb1(0))) ) )
=> ( $lesseq(0,20)
& $less(20,81)
& ! [Ss20: map_int_int] :
( ( $lesseq(0,81)
& ( Ss20 = tb2t(set(int,int,t2tb(Ss19),t2tb1(20),t2tb1(0))) ) )
=> ( $lesseq(0,21)
& $less(21,81)
& ! [Ss21: map_int_int] :
( ( $lesseq(0,81)
& ( Ss21 = tb2t(set(int,int,t2tb(Ss20),t2tb1(21),t2tb1(3))) ) )
=> ( $lesseq(0,22)
& $less(22,81)
& ! [Ss22: map_int_int] :
( ( $lesseq(0,81)
& ( Ss22 = tb2t(set(int,int,t2tb(Ss21),t2tb1(22),t2tb1(3))) ) )
=> ( $lesseq(0,23)
& $less(23,81)
& ! [Ss23: map_int_int] :
( ( $lesseq(0,81)
& ( Ss23 = tb2t(set(int,int,t2tb(Ss22),t2tb1(23),t2tb1(3))) ) )
=> ( $lesseq(0,24)
& $less(24,81)
& ! [Ss24: map_int_int] :
( ( $lesseq(0,81)
& ( Ss24 = tb2t(set(int,int,t2tb(Ss23),t2tb1(24),t2tb1(6))) ) )
=> ( $lesseq(0,25)
& $less(25,81)
& ! [Ss25: map_int_int] :
( ( $lesseq(0,81)
& ( Ss25 = tb2t(set(int,int,t2tb(Ss24),t2tb1(25),t2tb1(6))) ) )
=> ( $lesseq(0,26)
& $less(26,81)
& ! [Ss26: map_int_int] :
( ( $lesseq(0,81)
& ( Ss26 = tb2t(set(int,int,t2tb(Ss25),t2tb1(26),t2tb1(6))) ) )
=> ( $lesseq(0,27)
& $less(27,81)
& ! [Ss27: map_int_int] :
( ( $lesseq(0,81)
& ( Ss27 = tb2t(set(int,int,t2tb(Ss26),t2tb1(27),t2tb1(27))) ) )
=> ( $lesseq(0,28)
& $less(28,81)
& ! [Ss28: map_int_int] :
( ( $lesseq(0,81)
& ( Ss28 = tb2t(set(int,int,t2tb(Ss27),t2tb1(28),t2tb1(27))) ) )
=> ( $lesseq(0,29)
& $less(29,81)
& ! [Ss29: map_int_int] :
( ( $lesseq(0,81)
& ( Ss29 = tb2t(set(int,int,t2tb(Ss28),t2tb1(29),t2tb1(27))) ) )
=> ( $lesseq(0,30)
& $less(30,81)
& ! [Ss30: map_int_int] :
( ( $lesseq(0,81)
& ( Ss30 = tb2t(set(int,int,t2tb(Ss29),t2tb1(30),t2tb1(30))) ) )
=> ( $lesseq(0,31)
& $less(31,81)
& ! [Ss31: map_int_int] :
( ( $lesseq(0,81)
& ( Ss31 = tb2t(set(int,int,t2tb(Ss30),t2tb1(31),t2tb1(30))) ) )
=> ( $lesseq(0,32)
& $less(32,81)
& ! [Ss32: map_int_int] :
( ( $lesseq(0,81)
& ( Ss32 = tb2t(set(int,int,t2tb(Ss31),t2tb1(32),t2tb1(30))) ) )
=> ( $lesseq(0,33)
& $less(33,81)
& ! [Ss33: map_int_int] :
( ( $lesseq(0,81)
& ( Ss33 = tb2t(set(int,int,t2tb(Ss32),t2tb1(33),t2tb1(33))) ) )
=> ( $lesseq(0,34)
& $less(34,81)
& ! [Ss34: map_int_int] :
( ( $lesseq(0,81)
& ( Ss34 = tb2t(set(int,int,t2tb(Ss33),t2tb1(34),t2tb1(33))) ) )
=> ( $lesseq(0,35)
& $less(35,81)
& ! [Ss35: map_int_int] :
( ( $lesseq(0,81)
& ( Ss35 = tb2t(set(int,int,t2tb(Ss34),t2tb1(35),t2tb1(33))) ) )
=> ( $lesseq(0,36)
& $less(36,81)
& ! [Ss36: map_int_int] :
( ( $lesseq(0,81)
& ( Ss36 = tb2t(set(int,int,t2tb(Ss35),t2tb1(36),t2tb1(27))) ) )
=> ( $lesseq(0,37)
& $less(37,81)
& ! [Ss37: map_int_int] :
( ( $lesseq(0,81)
& ( Ss37 = tb2t(set(int,int,t2tb(Ss36),t2tb1(37),t2tb1(27))) ) )
=> ( $lesseq(0,38)
& $less(38,81)
& ! [Ss38: map_int_int] :
( ( $lesseq(0,81)
& ( Ss38 = tb2t(set(int,int,t2tb(Ss37),t2tb1(38),t2tb1(27))) ) )
=> ( $lesseq(0,39)
& $less(39,81)
& ! [Ss39: map_int_int] :
( ( $lesseq(0,81)
& ( Ss39 = tb2t(set(int,int,t2tb(Ss38),t2tb1(39),t2tb1(30))) ) )
=> ( $lesseq(0,40)
& $less(40,81)
& ! [Ss40: map_int_int] :
( ( $lesseq(0,81)
& ( Ss40 = tb2t(set(int,int,t2tb(Ss39),t2tb1(40),t2tb1(30))) ) )
=> ( $lesseq(0,41)
& $less(41,81)
& ! [Ss41: map_int_int] :
( ( $lesseq(0,81)
& ( Ss41 = tb2t(set(int,int,t2tb(Ss40),t2tb1(41),t2tb1(30))) ) )
=> ( $lesseq(0,42)
& $less(42,81)
& ! [Ss42: map_int_int] :
( ( $lesseq(0,81)
& ( Ss42 = tb2t(set(int,int,t2tb(Ss41),t2tb1(42),t2tb1(33))) ) )
=> ( $lesseq(0,43)
& $less(43,81)
& ! [Ss43: map_int_int] :
( ( $lesseq(0,81)
& ( Ss43 = tb2t(set(int,int,t2tb(Ss42),t2tb1(43),t2tb1(33))) ) )
=> ( $lesseq(0,44)
& $less(44,81)
& ! [Ss44: map_int_int] :
( ( $lesseq(0,81)
& ( Ss44 = tb2t(set(int,int,t2tb(Ss43),t2tb1(44),t2tb1(33))) ) )
=> ( $lesseq(0,45)
& $less(45,81)
& ! [Ss45: map_int_int] :
( ( $lesseq(0,81)
& ( Ss45 = tb2t(set(int,int,t2tb(Ss44),t2tb1(45),t2tb1(27))) ) )
=> ( $lesseq(0,46)
& $less(46,81)
& ! [Ss46: map_int_int] :
( ( $lesseq(0,81)
& ( Ss46 = tb2t(set(int,int,t2tb(Ss45),t2tb1(46),t2tb1(27))) ) )
=> ( $lesseq(0,47)
& $less(47,81)
& ! [Ss47: map_int_int] :
( ( $lesseq(0,81)
& ( Ss47 = tb2t(set(int,int,t2tb(Ss46),t2tb1(47),t2tb1(27))) ) )
=> ( $lesseq(0,48)
& $less(48,81)
& ! [Ss48: map_int_int] :
( ( $lesseq(0,81)
& ( Ss48 = tb2t(set(int,int,t2tb(Ss47),t2tb1(48),t2tb1(30))) ) )
=> ( $lesseq(0,49)
& $less(49,81)
& ! [Ss49: map_int_int] :
( ( $lesseq(0,81)
& ( Ss49 = tb2t(set(int,int,t2tb(Ss48),t2tb1(49),t2tb1(30))) ) )
=> ( $lesseq(0,50)
& $less(50,81)
& ! [Ss50: map_int_int] :
( ( $lesseq(0,81)
& ( Ss50 = tb2t(set(int,int,t2tb(Ss49),t2tb1(50),t2tb1(30))) ) )
=> ( $lesseq(0,51)
& $less(51,81)
& ! [Ss51: map_int_int] :
( ( $lesseq(0,81)
& ( Ss51 = tb2t(set(int,int,t2tb(Ss50),t2tb1(51),t2tb1(33))) ) )
=> ( $lesseq(0,52)
& $less(52,81)
& ! [Ss52: map_int_int] :
( ( $lesseq(0,81)
& ( Ss52 = tb2t(set(int,int,t2tb(Ss51),t2tb1(52),t2tb1(33))) ) )
=> ( $lesseq(0,53)
& $less(53,81)
& ! [Ss53: map_int_int] :
( ( $lesseq(0,81)
& ( Ss53 = tb2t(set(int,int,t2tb(Ss52),t2tb1(53),t2tb1(33))) ) )
=> ( $lesseq(0,54)
& $less(54,81)
& ! [Ss54: map_int_int] :
( ( $lesseq(0,81)
& ( Ss54 = tb2t(set(int,int,t2tb(Ss53),t2tb1(54),t2tb1(54))) ) )
=> ( $lesseq(0,55)
& $less(55,81)
& ! [Ss55: map_int_int] :
( ( $lesseq(0,81)
& ( Ss55 = tb2t(set(int,int,t2tb(Ss54),t2tb1(55),t2tb1(54))) ) )
=> ( $lesseq(0,56)
& $less(56,81)
& ! [Ss56: map_int_int] :
( ( $lesseq(0,81)
& ( Ss56 = tb2t(set(int,int,t2tb(Ss55),t2tb1(56),t2tb1(54))) ) )
=> ( $lesseq(0,57)
& $less(57,81)
& ! [Ss57: map_int_int] :
( ( $lesseq(0,81)
& ( Ss57 = tb2t(set(int,int,t2tb(Ss56),t2tb1(57),t2tb1(57))) ) )
=> ( $lesseq(0,58)
& $less(58,81)
& ! [Ss58: map_int_int] :
( ( $lesseq(0,81)
& ( Ss58 = tb2t(set(int,int,t2tb(Ss57),t2tb1(58),t2tb1(57))) ) )
=> ( $lesseq(0,59)
& $less(59,81)
& ! [Ss59: map_int_int] :
( ( $lesseq(0,81)
& ( Ss59 = tb2t(set(int,int,t2tb(Ss58),t2tb1(59),t2tb1(57))) ) )
=> ( $lesseq(0,60)
& $less(60,81)
& ! [Ss60: map_int_int] :
( ( $lesseq(0,81)
& ( Ss60 = tb2t(set(int,int,t2tb(Ss59),t2tb1(60),t2tb1(60))) ) )
=> ( $lesseq(0,61)
& $less(61,81)
& ! [Ss61: map_int_int] :
( ( $lesseq(0,81)
& ( Ss61 = tb2t(set(int,int,t2tb(Ss60),t2tb1(61),t2tb1(60))) ) )
=> ( $lesseq(0,62)
& $less(62,81)
& ! [Ss62: map_int_int] :
( ( $lesseq(0,81)
& ( Ss62 = tb2t(set(int,int,t2tb(Ss61),t2tb1(62),t2tb1(60))) ) )
=> ( $lesseq(0,63)
& $less(63,81)
& ! [Ss63: map_int_int] :
( ( $lesseq(0,81)
& ( Ss63 = tb2t(set(int,int,t2tb(Ss62),t2tb1(63),t2tb1(54))) ) )
=> ( $lesseq(0,64)
& $less(64,81)
& ! [Ss64: map_int_int] :
( ( $lesseq(0,81)
& ( Ss64 = tb2t(set(int,int,t2tb(Ss63),t2tb1(64),t2tb1(54))) ) )
=> ( $lesseq(0,65)
& $less(65,81)
& ! [Ss65: map_int_int] :
( ( $lesseq(0,81)
& ( Ss65 = tb2t(set(int,int,t2tb(Ss64),t2tb1(65),t2tb1(54))) ) )
=> ( $lesseq(0,66)
& $less(66,81)
& ! [Ss66: map_int_int] :
( ( $lesseq(0,81)
& ( Ss66 = tb2t(set(int,int,t2tb(Ss65),t2tb1(66),t2tb1(57))) ) )
=> ( $lesseq(0,67)
& $less(67,81)
& ! [Ss67: map_int_int] :
( ( $lesseq(0,81)
& ( Ss67 = tb2t(set(int,int,t2tb(Ss66),t2tb1(67),t2tb1(57))) ) )
=> ( $lesseq(0,68)
& $less(68,81)
& ! [Ss68: map_int_int] :
( ( $lesseq(0,81)
& ( Ss68 = tb2t(set(int,int,t2tb(Ss67),t2tb1(68),t2tb1(57))) ) )
=> ( $lesseq(0,69)
& $less(69,81)
& ! [Ss69: map_int_int] :
( ( $lesseq(0,81)
& ( Ss69 = tb2t(set(int,int,t2tb(Ss68),t2tb1(69),t2tb1(60))) ) )
=> ( $lesseq(0,70)
& $less(70,81)
& ! [Ss70: map_int_int] :
( ( $lesseq(0,81)
& ( Ss70 = tb2t(set(int,int,t2tb(Ss69),t2tb1(70),t2tb1(60))) ) )
=> ( $lesseq(0,71)
& $less(71,81)
& ! [Ss71: map_int_int] :
( ( $lesseq(0,81)
& ( Ss71 = tb2t(set(int,int,t2tb(Ss70),t2tb1(71),t2tb1(60))) ) )
=> ( $lesseq(0,72)
& $less(72,81)
& ! [Ss72: map_int_int] :
( ( $lesseq(0,81)
& ( Ss72 = tb2t(set(int,int,t2tb(Ss71),t2tb1(72),t2tb1(54))) ) )
=> ( $lesseq(0,73)
& $less(73,81)
& ! [Ss73: map_int_int] :
( ( $lesseq(0,81)
& ( Ss73 = tb2t(set(int,int,t2tb(Ss72),t2tb1(73),t2tb1(54))) ) )
=> ( $lesseq(0,74)
& $less(74,81)
& ! [Ss74: map_int_int] :
( ( $lesseq(0,81)
& ( Ss74 = tb2t(set(int,int,t2tb(Ss73),t2tb1(74),t2tb1(54))) ) )
=> ( $lesseq(0,75)
& $less(75,81)
& ! [Ss75: map_int_int] :
( ( $lesseq(0,81)
& ( Ss75 = tb2t(set(int,int,t2tb(Ss74),t2tb1(75),t2tb1(57))) ) )
=> ( $lesseq(0,76)
& $less(76,81)
& ! [Ss76: map_int_int] :
( ( $lesseq(0,81)
& ( Ss76 = tb2t(set(int,int,t2tb(Ss75),t2tb1(76),t2tb1(57))) ) )
=> ( $lesseq(0,77)
& $less(77,81)
& ! [Ss77: map_int_int] :
( ( $lesseq(0,81)
& ( Ss77 = tb2t(set(int,int,t2tb(Ss76),t2tb1(77),t2tb1(57))) ) )
=> ( $lesseq(0,78)
& $less(78,81)
& ! [Ss78: map_int_int] :
( ( $lesseq(0,81)
& ( Ss78 = tb2t(set(int,int,t2tb(Ss77),t2tb1(78),t2tb1(60))) ) )
=> ( $lesseq(0,79)
& $less(79,81)
& ! [Ss79: map_int_int] :
( ( $lesseq(0,81)
& ( Ss79 = tb2t(set(int,int,t2tb(Ss78),t2tb1(79),t2tb1(60))) ) )
=> ( $lesseq(0,80)
& $less(80,81)
& ! [Ss80: map_int_int] :
( ( $lesseq(0,81)
& ( Ss80 = tb2t(set(int,int,t2tb(Ss79),t2tb1(80),t2tb1(60))) ) )
=> ( $lesseq(0,9)
& ( $lesseq(0,9)
=> ( $lesseq(0,0)
& $less(0,9)
& ! [So: map_int_int] :
( ( $lesseq(0,9)
& ( So = tb2t(set(int,int,const(int,int,t2tb1(0)),t2tb1(0),t2tb1(0))) ) )
=> ( $lesseq(0,1)
& $less(1,9)
& ! [So1: map_int_int] :
( ( $lesseq(0,9)
& ( So1 = tb2t(set(int,int,t2tb(So),t2tb1(1),t2tb1(1))) ) )
=> ( $lesseq(0,2)
& $less(2,9)
& ! [So2: map_int_int] :
( ( $lesseq(0,9)
& ( So2 = tb2t(set(int,int,t2tb(So1),t2tb1(2),t2tb1(2))) ) )
=> ( $lesseq(0,3)
& $less(3,9)
& ! [So3: map_int_int] :
( ( $lesseq(0,9)
& ( So3 = tb2t(set(int,int,t2tb(So2),t2tb1(3),t2tb1(9))) ) )
=> ( $lesseq(0,4)
& $less(4,9)
& ! [So4: map_int_int] :
( ( $lesseq(0,9)
& ( So4 = tb2t(set(int,int,t2tb(So3),t2tb1(4),t2tb1(10))) ) )
=> ( $lesseq(0,5)
& $less(5,9)
& ! [So5: map_int_int] :
( ( $lesseq(0,9)
& ( So5 = tb2t(set(int,int,t2tb(So4),t2tb1(5),t2tb1(11))) ) )
=> ( $lesseq(0,6)
& $less(6,9)
& ! [So6: map_int_int] :
( ( $lesseq(0,9)
& ( So6 = tb2t(set(int,int,t2tb(So5),t2tb1(6),t2tb1(18))) ) )
=> ( $lesseq(0,7)
& $less(7,9)
& ! [So7: map_int_int] :
( ( $lesseq(0,9)
& ( So7 = tb2t(set(int,int,t2tb(So6),t2tb1(7),t2tb1(19))) ) )
=> ( $lesseq(0,8)
& $less(8,9)
& ! [So8: map_int_int] :
( ( $lesseq(0,9)
& ( So8 = tb2t(set(int,int,t2tb(So7),t2tb1(8),t2tb1(20))) ) )
=> well_formed_sudoku1(mk_sudoku_chunks1(tb2t2(mk_array1(int,81,t2tb(Cs80))),tb2t2(mk_array1(int,9,t2tb(Co8))),tb2t2(mk_array1(int,81,t2tb(Rs80))),tb2t2(mk_array1(int,9,t2tb(Ro8))),tb2t2(mk_array1(int,81,t2tb(Ss80))),tb2t2(mk_array1(int,9,t2tb(So8))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------