%   ORIGINAL: 'h4/thm/list/MAP_EQ_EVERY2_'
% Assm: HL_TRUTH: T
% Assm: HL_FALSITY: ~F
% Assm: HL_BOOL_CASES: !t. (t <=> T) \/ (t <=> F)
% Assm: HL_EXT: !f g. (!x. f x = g x) ==> f = g
% Goal: !f1 f2 l1 l2. 'h4/const/list/MAP' f1 l1 = 'h4/const/list/MAP' f2 l2 <=> 'h4/const/list/LENGTH' l1 = 'h4/const/list/LENGTH' l2 /\ 'h4/const/list/LIST_REL' (\x y. f1 x = f2 y) l1 l2
%   PROCESSED
% Assm ['HL_TRUTH']: T
% Assm ['HL_FALSITY']: ~F
% Assm ['HL_BOOL_CASES']: !t. (t <=> T) \/ (t <=> F)
% Assm ['HL_EXT']: !f g. (!x. happ f x = happ g x) ==> f = g
% Goal: !_1. (!f1 x f2 y. happ (happ (happ (happ _1 f1) x) f2) y <=> happ f1 x = happ f2 y) ==> (!_0. (!f1 f2 x. happ (happ (happ _0 f1) f2) x = happ (happ (happ _1 f1) x) f2) ==> (!f1 f2 l1 l2. 'h4/const/list/MAP' f1 l1 = 'h4/const/list/MAP' f2 l2 <=> 'h4/const/list/LENGTH' l1 = 'h4/const/list/LENGTH' l2 /\ 'h4/const/list/LIST_REL' (happ (happ _0 f1) f2) l1 l2))
fof('HL_TRUTH', axiom, p(s(bool,'T'))).
fof('HL_FALSITY', axiom, ~ (p(s(bool,'F')))).
fof('HL_BOOL_CASES', axiom, ![T]: (s(bool,T) = s(bool,'T') | s(bool,T) = s(bool,'F'))).
fof('HL_EXT', axiom, ![V_3f7515,V_3f7511]: ![F, G]: (![X]: s(V_3f7511,happ(s(fun(V_3f7515,V_3f7511),F),s(V_3f7515,X))) = s(V_3f7511,happ(s(fun(V_3f7515,V_3f7511),G),s(V_3f7515,X))) => s(fun(V_3f7515,V_3f7511),F) = s(fun(V_3f7515,V_3f7511),G))).
fof('h4/thm/list/MAP_EQ_EVERY2_', conjecture, ![B,A,C]: ![V__1]: (![F1, X, F2, Y]: (p(s(bool,happ(s(fun(C,bool),happ(s(fun(fun(C,B),fun(C,bool)),happ(s(fun(A,fun(fun(C,B),fun(C,bool))),happ(s(fun(fun(A,B),fun(A,fun(fun(C,B),fun(C,bool)))),V__1),s(fun(A,B),F1))),s(A,X))),s(fun(C,B),F2))),s(C,Y)))) <=> s(B,happ(s(fun(A,B),F1),s(A,X))) = s(B,happ(s(fun(C,B),F2),s(C,Y)))) => ![V__0]: (![F1, F2, X]: s(fun(C,bool),happ(s(fun(A,fun(C,bool)),happ(s(fun(fun(C,B),fun(A,fun(C,bool))),happ(s(fun(fun(A,B),fun(fun(C,B),fun(A,fun(C,bool)))),V__0),s(fun(A,B),F1))),s(fun(C,B),F2))),s(A,X))) = s(fun(C,bool),happ(s(fun(fun(C,B),fun(C,bool)),happ(s(fun(A,fun(fun(C,B),fun(C,bool))),happ(s(fun(fun(A,B),fun(A,fun(fun(C,B),fun(C,bool)))),V__1),s(fun(A,B),F1))),s(A,X))),s(fun(C,B),F2))) => ![F1, F2, L1, L2]: (s('h4/type/list/list'(B),'h4/const/list/MAP'(s(fun(A,B),F1),s('h4/type/list/list'(A),L1))) = s('h4/type/list/list'(B),'h4/const/list/MAP'(s(fun(C,B),F2),s('h4/type/list/list'(C),L2))) <=> (s('h4/type/num/num','h4/const/list/LENGTH'(s('h4/type/list/list'(A),L1))) = s('h4/type/num/num','h4/const/list/LENGTH'(s('h4/type/list/list'(C),L2))) & p(s(bool,'h4/const/list/LIST_REL'(s(fun(A,fun(C,bool)),happ(s(fun(fun(C,B),fun(A,fun(C,bool))),happ(s(fun(fun(A,B),fun(fun(C,B),fun(A,fun(C,bool)))),V__0),s(fun(A,B),F1))),s(fun(C,B),F2))),s('h4/type/list/list'(A),L1),s('h4/type/list/list'(C),L2))))))))).
