TPTP Problem File: SWW618_2.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : SWW618_2 : TPTP v8.2.0. Released v6.1.0.
% Domain : Software Verification
% Problem : Max matrix-T-WP parameter maxmat
% 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 : max_matrix-T-WP_parameter_maxmat [Fil14]
% Status : Theorem
% Rating : 0.62 v8.2.0, 0.88 v7.5.0, 0.90 v7.4.0, 0.75 v7.3.0, 0.67 v7.1.0, 0.83 v7.0.0, 0.71 v6.4.0, 0.67 v6.3.0, 0.71 v6.2.0, 0.88 v6.1.0
% Syntax : Number of formulae : 173 ( 50 unt; 77 typ; 0 def)
% Number of atoms : 185 ( 72 equ)
% Maximal formula atoms : 12 ( 1 avg)
% Number of connectives : 96 ( 7 ~; 4 |; 26 &)
% ( 7 <=>; 52 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 6 ( 1 avg)
% Number arithmetic : 147 ( 53 atm; 12 fun; 22 num; 60 var)
% Number of types : 14 ( 12 usr; 1 ari)
% Number of type conns : 100 ( 53 >; 47 *; 0 +; 0 <<)
% Number of predicates : 9 ( 6 usr; 0 prp; 1-2 aty)
% Number of functors : 64 ( 59 usr; 14 con; 0-5 aty)
% Number of variables : 223 ( 223 !; 0 ?; 223 :)
% SPC : TF0_THM_EQU_ARI
% Comments :
%------------------------------------------------------------------------------
tff(uni,type,
uni: $tType ).
tff(ty,type,
ty: $tType ).
tff(sort,type,
sort: ( ty * uni ) > $o ).
tff(witness,type,
witness: ty > uni ).
tff(witness_sort,axiom,
! [A: ty] : sort(A,witness(A)) ).
tff(int,type,
int: ty ).
tff(real,type,
real: ty ).
tff(bool,type,
bool: $tType ).
tff(bool1,type,
bool1: ty ).
tff(true,type,
true: bool ).
tff(false,type,
false: bool ).
tff(match_bool,type,
match_bool: ( ty * bool * uni * uni ) > uni ).
tff(match_bool_sort,axiom,
! [A: ty,X: bool,X1: uni,X2: uni] : sort(A,match_bool(A,X,X1,X2)) ).
tff(match_bool_True,axiom,
! [A: ty,Z: uni,Z1: uni] :
( sort(A,Z)
=> ( match_bool(A,true,Z,Z1) = Z ) ) ).
tff(match_bool_False,axiom,
! [A: ty,Z: uni,Z1: uni] :
( sort(A,Z1)
=> ( match_bool(A,false,Z,Z1) = Z1 ) ) ).
tff(true_False,axiom,
true != false ).
tff(bool_inversion,axiom,
! [U: bool] :
( ( U = true )
| ( U = false ) ) ).
tff(tuple0,type,
tuple0: $tType ).
tff(tuple01,type,
tuple01: ty ).
tff(tuple02,type,
tuple02: tuple0 ).
tff(tuple0_inversion,axiom,
! [U: tuple0] : U = tuple02 ).
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(min,type,
min: ( $int * $int ) > $int ).
tff(max,type,
max: ( $int * $int ) > $int ).
tff(max_is_ge,axiom,
! [X: $int,Y: $int] :
( $lesseq(X,max(X,Y))
& $lesseq(Y,max(X,Y)) ) ).
tff(max_is_some,axiom,
! [X: $int,Y: $int] :
( ( max(X,Y) = X )
| ( max(X,Y) = Y ) ) ).
tff(min_is_le,axiom,
! [X: $int,Y: $int] :
( $lesseq(min(X,Y),X)
& $lesseq(min(X,Y),Y) ) ).
tff(min_is_some,axiom,
! [X: $int,Y: $int] :
( ( min(X,Y) = X )
| ( min(X,Y) = Y ) ) ).
tff(max_x,axiom,
! [X: $int,Y: $int] :
( $lesseq(Y,X)
=> ( max(X,Y) = X ) ) ).
tff(max_y,axiom,
! [X: $int,Y: $int] :
( $lesseq(X,Y)
=> ( max(X,Y) = Y ) ) ).
tff(min_x,axiom,
! [X: $int,Y: $int] :
( $lesseq(X,Y)
=> ( min(X,Y) = X ) ) ).
tff(min_y,axiom,
! [X: $int,Y: $int] :
( $lesseq(Y,X)
=> ( min(X,Y) = Y ) ) ).
tff(max_sym,axiom,
! [X: $int,Y: $int] :
( $lesseq(Y,X)
=> ( max(X,Y) = max(Y,X) ) ) ).
tff(min_sym,axiom,
! [X: $int,Y: $int] :
( $lesseq(Y,X)
=> ( min(X,Y) = min(Y,X) ) ) ).
tff(map,type,
map: ( ty * ty ) > ty ).
tff(get,type,
get: ( ty * ty * uni * uni ) > uni ).
tff(get_sort,axiom,
! [A: ty,B: ty,X: uni,X1: uni] : sort(B,get(B,A,X,X1)) ).
tff(set,type,
set: ( ty * ty * uni * uni * uni ) > uni ).
tff(set_sort,axiom,
! [A: ty,B: ty,X: uni,X1: uni,X2: uni] : sort(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] :
( sort(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] :
( sort(A,A1)
=> ( sort(A,A2)
=> ! [B1: uni] :
( ( A1 != A2 )
=> ( get(B,A,set(B,A,M,A1,B1),A2) = get(B,A,M,A2) ) ) ) ) ).
tff(const,type,
const: ( ty * ty * uni ) > uni ).
tff(const_sort,axiom,
! [A: ty,B: ty,X: uni] : sort(map(A,B),const(B,A,X)) ).
tff(const1,axiom,
! [A: ty,B: ty,B1: uni,A1: uni] :
( sort(B,B1)
=> ( get(B,A,const(B,A,B1),A1) = B1 ) ) ).
tff(ref,type,
ref: ty > ty ).
tff(mk_ref,type,
mk_ref: ( ty * uni ) > uni ).
tff(mk_ref_sort,axiom,
! [A: ty,X: uni] : sort(ref(A),mk_ref(A,X)) ).
tff(contents,type,
contents: ( ty * uni ) > uni ).
tff(contents_sort,axiom,
! [A: ty,X: uni] : sort(A,contents(A,X)) ).
tff(contents_def,axiom,
! [A: ty,U: uni] :
( sort(A,U)
=> ( contents(A,mk_ref(A,U)) = U ) ) ).
tff(ref_inversion,axiom,
! [A: ty,U: uni] :
( sort(ref(A),U)
=> ( U = mk_ref(A,contents(A,U)) ) ) ).
tff(n,type,
n: $int ).
tff(n_nonneg,axiom,
$lesseq(0,n) ).
tff(size,type,
size: $int ).
tff(set1,type,
set1: $tType ).
tff(set2,type,
set2: ty ).
tff(mem,type,
mem: ( $int * set1 ) > $o ).
tff(remove,type,
remove: ( $int * set1 ) > set1 ).
tff(remove_def1,axiom,
! [X: $int,Y: $int,S: set1] :
( mem(X,remove(Y,S))
<=> ( ( X != Y )
& mem(X,S) ) ) ).
tff(below,type,
below: $int > set1 ).
tff(below_def,axiom,
! [X: $int,N: $int] :
( ( $lesseq(0,N)
& $lesseq(N,size) )
=> ( mem(X,below(N))
<=> ( $lesseq(0,X)
& $less(X,N) ) ) ) ).
tff(cardinal,type,
cardinal: set1 > $int ).
tff(cardinal_empty,axiom,
! [S: set1] :
( ( cardinal(S) = 0 )
<=> ! [X: $int] : ~ mem(X,S) ) ).
tff(cardinal_remove,axiom,
! [X: $int,S: set1] :
( mem(X,S)
=> ( cardinal(S) = $sum(1,cardinal(remove(X,S))) ) ) ).
tff(cardinal_below,axiom,
! [N: $int] :
( ( $lesseq(0,N)
& $lesseq(N,size) )
=> ( ( $lesseq(0,N)
=> ( cardinal(below(N)) = N ) )
& ( ~ $lesseq(0,N)
=> ( cardinal(below(N)) = 0 ) ) ) ) ).
tff(integer_size,axiom,
$lesseq(n,size) ).
tff(map_int_lpmap_int_intrp,type,
map_int_lpmap_int_intrp: $tType ).
tff(m,type,
m: map_int_lpmap_int_intrp ).
tff(map_int_int,type,
map_int_int: $tType ).
tff(t2tb,type,
t2tb: map_int_int > uni ).
tff(t2tb_sort,axiom,
! [X: map_int_int] : sort(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: map_int_lpmap_int_intrp > uni ).
tff(t2tb_sort1,axiom,
! [X: map_int_lpmap_int_intrp] : sort(map(int,map(int,int)),t2tb1(X)) ).
tff(tb2t1,type,
tb2t1: uni > map_int_lpmap_int_intrp ).
tff(bridgeL1,axiom,
! [I: map_int_lpmap_int_intrp] : tb2t1(t2tb1(I)) = I ).
tff(bridgeR1,axiom,
! [J: uni] : t2tb1(tb2t1(J)) = J ).
tff(t2tb2,type,
t2tb2: $int > uni ).
tff(t2tb_sort2,axiom,
! [X: $int] : sort(int,t2tb2(X)) ).
tff(tb2t2,type,
tb2t2: uni > $int ).
tff(bridgeL2,axiom,
! [I: $int] : tb2t2(t2tb2(I)) = I ).
tff(bridgeR2,axiom,
! [J: uni] : t2tb2(tb2t2(J)) = J ).
tff(m_pos,axiom,
! [I: $int,J: $int] :
( ( $lesseq(0,I)
& $less(I,n) )
=> ( ( $lesseq(0,J)
& $less(J,n) )
=> $lesseq(0,tb2t2(get(int,int,get(map(int,int),int,t2tb1(m),t2tb2(I)),t2tb2(J)))) ) ) ).
tff(solution,type,
solution: ( map_int_int * $int ) > $o ).
tff(solution_def,axiom,
! [S: map_int_int,I: $int] :
( solution(S,I)
<=> ( ! [K: $int] :
( ( $lesseq(I,K)
& $less(K,n) )
=> ( $lesseq(0,tb2t2(get(int,int,t2tb(S),t2tb2(K))))
& $less(tb2t2(get(int,int,t2tb(S),t2tb2(K))),n) ) )
& ! [K1: $int,K2: $int] :
( ( $lesseq(I,K1)
& $less(K1,K2)
& $less(K2,n) )
=> ( tb2t2(get(int,int,t2tb(S),t2tb2(K1))) != tb2t2(get(int,int,t2tb(S),t2tb2(K2))) ) ) ) ) ).
tff(f,type,
f: ( map_int_int * $int ) > $int ).
tff(f_def,axiom,
! [S: map_int_int,I: $int] : f(S,I) = tb2t2(get(int,int,get(map(int,int),int,t2tb1(m),t2tb2(I)),get(int,int,t2tb(S),t2tb2(I)))) ).
tff(sum,type,
sum: ( map_int_int * $int * $int ) > $int ).
tff(sum_def_empty,axiom,
! [C: map_int_int,I: $int,J: $int] :
( $lesseq(J,I)
=> ( sum(C,I,J) = 0 ) ) ).
tff(sum_def_non_empty,axiom,
! [C: map_int_int,I: $int,J: $int] :
( $less(I,J)
=> ( sum(C,I,J) = $sum(f(C,I),sum(C,$sum(I,1),J)) ) ) ).
tff(sum_right_extension,axiom,
! [C: map_int_int,I: $int,J: $int] :
( $less(I,J)
=> ( sum(C,I,J) = $sum(sum(C,I,$difference(J,1)),f(C,$difference(J,1))) ) ) ).
tff(sum_transitivity,axiom,
! [C: map_int_int,I: $int,K: $int,J: $int] :
( ( $lesseq(I,K)
& $lesseq(K,J) )
=> ( sum(C,I,J) = $sum(sum(C,I,K),sum(C,K,J)) ) ) ).
tff(sum_eq,axiom,
! [C1: map_int_int,C2: map_int_int,I: $int,J: $int] :
( ! [K: $int] :
( ( $lesseq(I,K)
& $less(K,J) )
=> ( f(C1,K) = f(C2,K) ) )
=> ( sum(C1,I,J) = sum(C2,I,J) ) ) ).
tff(sum_ind,axiom,
! [I: $int] :
( $less(I,n)
=> ! [J: $int,S: map_int_int] : sum(tb2t(set(int,int,t2tb(S),t2tb2(I),t2tb2(J))),I,n) = $sum(tb2t2(get(int,int,get(map(int,int),int,t2tb1(m),t2tb2(I)),t2tb2(J))),sum(S,$sum(I,1),n)) ) ).
tff(option,type,
option: ty > ty ).
tff(none,type,
none: ty > uni ).
tff(none_sort,axiom,
! [A: ty] : sort(option(A),none(A)) ).
tff(some,type,
some: ( ty * uni ) > uni ).
tff(some_sort,axiom,
! [A: ty,X: uni] : sort(option(A),some(A,X)) ).
tff(match_option,type,
match_option: ( ty * ty * uni * uni * uni ) > uni ).
tff(match_option_sort,axiom,
! [A: ty,A1: ty,X: uni,X1: uni,X2: uni] : sort(A1,match_option(A1,A,X,X1,X2)) ).
tff(match_option_None,axiom,
! [A: ty,A1: ty,Z: uni,Z1: uni] :
( sort(A1,Z)
=> ( match_option(A1,A,none(A),Z,Z1) = Z ) ) ).
tff(match_option_Some,axiom,
! [A: ty,A1: ty,Z: uni,Z1: uni,U: uni] :
( sort(A1,Z1)
=> ( match_option(A1,A,some(A,U),Z,Z1) = Z1 ) ) ).
tff(none_Some,axiom,
! [A: ty,V: uni] : none(A) != some(A,V) ).
tff(some_proj_1,type,
some_proj_1: ( ty * uni ) > uni ).
tff(some_proj_1_sort,axiom,
! [A: ty,X: uni] : sort(A,some_proj_1(A,X)) ).
tff(some_proj_1_def,axiom,
! [A: ty,U: uni] :
( sort(A,U)
=> ( some_proj_1(A,some(A,U)) = U ) ) ).
tff(option_inversion,axiom,
! [A: ty,U: uni] :
( sort(option(A),U)
=> ( ( U = none(A) )
| ( U = some(A,some_proj_1(A,U)) ) ) ) ).
tff(t,type,
t: ( ty * ty ) > ty ).
tff(mk_t,type,
mk_t: ( ty * ty * uni ) > uni ).
tff(mk_t_sort,axiom,
! [A: ty,B: ty,X: uni] : sort(t(A,B),mk_t(B,A,X)) ).
tff(contents1,type,
contents1: ( ty * ty * uni ) > uni ).
tff(contents_sort1,axiom,
! [A: ty,B: ty,X: uni] : sort(map(A,option(B)),contents1(B,A,X)) ).
tff(contents_def1,axiom,
! [A: ty,B: ty,U: uni] :
( sort(map(A,option(B)),U)
=> ( contents1(B,A,mk_t(B,A,U)) = U ) ) ).
tff(t_inversion,axiom,
! [A: ty,B: ty,U: uni] :
( sort(t(A,B),U)
=> ( U = mk_t(B,A,contents1(B,A,U)) ) ) ).
tff(mixfix_lbrb,type,
mixfix_lbrb: ( ty * ty * uni * uni ) > uni ).
tff(mixfix_lbrb_sort,axiom,
! [A: ty,B: ty,X: uni,X1: uni] : sort(option(B),mixfix_lbrb(B,A,X,X1)) ).
tff(mixfix_lbrb_def,axiom,
! [A: ty,B: ty,H: uni,K: uni] : mixfix_lbrb(B,A,H,K) = get(option(B),A,contents1(B,A,H),K) ).
tff(tuple2,type,
tuple2: ( ty * ty ) > ty ).
tff(tuple21,type,
tuple21: ( ty * ty * uni * uni ) > uni ).
tff(tuple2_sort,axiom,
! [A: ty,A1: ty,X: uni,X1: uni] : sort(tuple2(A1,A),tuple21(A1,A,X,X1)) ).
tff(tuple2_proj_1,type,
tuple2_proj_1: ( ty * ty * uni ) > uni ).
tff(tuple2_proj_1_sort,axiom,
! [A: ty,A1: ty,X: uni] : sort(A1,tuple2_proj_1(A1,A,X)) ).
tff(tuple2_proj_1_def,axiom,
! [A: ty,A1: ty,U: uni,U1: uni] :
( sort(A1,U)
=> ( tuple2_proj_1(A1,A,tuple21(A1,A,U,U1)) = U ) ) ).
tff(tuple2_proj_2,type,
tuple2_proj_2: ( ty * ty * uni ) > uni ).
tff(tuple2_proj_2_sort,axiom,
! [A: ty,A1: ty,X: uni] : sort(A,tuple2_proj_2(A1,A,X)) ).
tff(tuple2_proj_2_def,axiom,
! [A: ty,A1: ty,U: uni,U1: uni] :
( sort(A,U1)
=> ( tuple2_proj_2(A1,A,tuple21(A1,A,U,U1)) = U1 ) ) ).
tff(tuple2_inversion,axiom,
! [A: ty,A1: ty,U: uni] :
( sort(tuple2(A1,A),U)
=> ( U = tuple21(A1,A,tuple2_proj_1(A1,A,U),tuple2_proj_2(A1,A,U)) ) ) ).
tff(lpintcm_setrp,type,
lpintcm_setrp: $tType ).
tff(pre,type,
pre: lpintcm_setrp > $o ).
tff(t2tb3,type,
t2tb3: lpintcm_setrp > uni ).
tff(t2tb_sort3,axiom,
! [X: lpintcm_setrp] : sort(tuple2(int,set2),t2tb3(X)) ).
tff(tb2t3,type,
tb2t3: uni > lpintcm_setrp ).
tff(bridgeL3,axiom,
! [I: lpintcm_setrp] : tb2t3(t2tb3(I)) = I ).
tff(bridgeR3,axiom,
! [J: uni] : t2tb3(tb2t3(J)) = J ).
tff(t2tb4,type,
t2tb4: set1 > uni ).
tff(t2tb_sort4,axiom,
! [X: set1] : sort(set2,t2tb4(X)) ).
tff(tb2t4,type,
tb2t4: uni > set1 ).
tff(bridgeL4,axiom,
! [I: set1] : tb2t4(t2tb4(I)) = I ).
tff(bridgeR4,axiom,
! [J: uni] :
( sort(set2,J)
=> ( t2tb4(tb2t4(J)) = J ) ) ).
tff(pre_def,axiom,
! [I: $int,C: set1] :
( pre(tb2t3(tuple21(int,set2,t2tb2(I),t2tb4(C))))
<=> ( $lesseq(0,I)
& $lesseq(I,n)
& ( cardinal(C) = $difference(n,I) )
& ! [K: $int] :
( mem(K,C)
=> ( $lesseq(0,K)
& $less(K,n) ) ) ) ) ).
tff(lpintcm_map_int_intrp,type,
lpintcm_map_int_intrp: $tType ).
tff(post,type,
post: ( lpintcm_setrp * lpintcm_map_int_intrp ) > $o ).
tff(t2tb5,type,
t2tb5: lpintcm_map_int_intrp > uni ).
tff(t2tb_sort5,axiom,
! [X: lpintcm_map_int_intrp] : sort(tuple2(int,map(int,int)),t2tb5(X)) ).
tff(tb2t5,type,
tb2t5: uni > lpintcm_map_int_intrp ).
tff(bridgeL5,axiom,
! [I: lpintcm_map_int_intrp] : tb2t5(t2tb5(I)) = I ).
tff(bridgeR5,axiom,
! [J: uni] : t2tb5(tb2t5(J)) = J ).
tff(post_def,axiom,
! [I: $int,C: set1,R: $int,Sol: map_int_int] :
( post(tb2t3(tuple21(int,set2,t2tb2(I),t2tb4(C))),tb2t5(tuple21(int,map(int,int),t2tb2(R),t2tb(Sol))))
<=> ( $lesseq(0,R)
& solution(Sol,I)
& ! [K: $int] :
( ( $lesseq(I,K)
& $less(K,n) )
=> mem(tb2t2(get(int,int,t2tb(Sol),t2tb2(K))),C) )
& ( R = sum(Sol,I,n) )
& ! [S: map_int_int] :
( solution(S,I)
=> ( ! [K: $int] :
( ( $lesseq(I,K)
& $less(K,n) )
=> mem(tb2t2(get(int,int,t2tb(S),t2tb2(K))),C) )
=> $lesseq(sum(S,I,n),R) ) ) ) ) ).
tff(t18_lpintcm_setrp_lpintcm_map_int_intrp,type,
t18_lpintcm_setrp_lpintcm_map_int_intrp: $tType ).
tff(inv,type,
inv: t18_lpintcm_setrp_lpintcm_map_int_intrp > $o ).
tff(option_lpintcm_map_int_intrp,type,
option_lpintcm_map_int_intrp: $tType ).
tff(t2tb6,type,
t2tb6: option_lpintcm_map_int_intrp > uni ).
tff(t2tb_sort6,axiom,
! [X: option_lpintcm_map_int_intrp] : sort(option(tuple2(int,map(int,int))),t2tb6(X)) ).
tff(tb2t6,type,
tb2t6: uni > option_lpintcm_map_int_intrp ).
tff(bridgeL6,axiom,
! [I: option_lpintcm_map_int_intrp] : tb2t6(t2tb6(I)) = I ).
tff(bridgeR6,axiom,
! [J: uni] : t2tb6(tb2t6(J)) = J ).
tff(t2tb7,type,
t2tb7: t18_lpintcm_setrp_lpintcm_map_int_intrp > uni ).
tff(t2tb_sort7,axiom,
! [X: t18_lpintcm_setrp_lpintcm_map_int_intrp] : sort(t(tuple2(int,set2),tuple2(int,map(int,int))),t2tb7(X)) ).
tff(tb2t7,type,
tb2t7: uni > t18_lpintcm_setrp_lpintcm_map_int_intrp ).
tff(bridgeL7,axiom,
! [I: t18_lpintcm_setrp_lpintcm_map_int_intrp] : tb2t7(t2tb7(I)) = I ).
tff(bridgeR7,axiom,
! [J: uni] : t2tb7(tb2t7(J)) = J ).
tff(inv_def,axiom,
! [T: t18_lpintcm_setrp_lpintcm_map_int_intrp] :
( inv(T)
<=> ! [K: lpintcm_setrp,V: lpintcm_map_int_intrp] :
( ( tb2t6(mixfix_lbrb(tuple2(int,map(int,int)),tuple2(int,set2),t2tb7(T),t2tb3(K))) = tb2t6(some(tuple2(int,map(int,int)),t2tb5(V))) )
=> post(K,V) ) ) ).
tff(map_lpintcm_setrp_lpoption_lpintcm_map_int_intrprp,type,
map_lpintcm_setrp_lpoption_lpintcm_map_int_intrprp: $tType ).
tff(t2tb8,type,
t2tb8: map_lpintcm_setrp_lpoption_lpintcm_map_int_intrprp > uni ).
tff(t2tb_sort8,axiom,
! [X: map_lpintcm_setrp_lpoption_lpintcm_map_int_intrprp] : sort(map(tuple2(int,set2),option(tuple2(int,map(int,int)))),t2tb8(X)) ).
tff(tb2t8,type,
tb2t8: uni > map_lpintcm_setrp_lpoption_lpintcm_map_int_intrprp ).
tff(bridgeL8,axiom,
! [I: map_lpintcm_setrp_lpoption_lpintcm_map_int_intrprp] : tb2t8(t2tb8(I)) = I ).
tff(bridgeR8,axiom,
! [J: uni] : t2tb8(tb2t8(J)) = J ).
tff(wP_parameter_maxmat,conjecture,
! [Table: map_lpintcm_setrp_lpoption_lpintcm_map_int_intrprp] :
( ! [K: $int,K1: set1] : tb2t6(get(option(tuple2(int,map(int,int))),tuple2(int,set2),t2tb8(Table),tuple21(int,set2,t2tb2(K),t2tb4(K1)))) = tb2t6(none(tuple2(int,map(int,int))))
=> ! [K: lpintcm_setrp,V: lpintcm_map_int_intrp] :
( ( tb2t6(mixfix_lbrb(tuple2(int,map(int,int)),tuple2(int,set2),mk_t(tuple2(int,map(int,int)),tuple2(int,set2),t2tb8(Table)),t2tb3(K))) = tb2t6(some(tuple2(int,map(int,int)),t2tb5(V))) )
=> post(K,V) ) ) ).
%------------------------------------------------------------------------------