%   ORIGINAL: 'h4/thm/list/EVERY2_MAP_0'
% 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: !l2 l1 f P. 'h4/const/list/LIST_REL' P ('h4/const/list/MAP' f l1) l2 <=> 'h4/const/list/LIST_REL' (\x y. P (f x) 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. (!P f x y. happ (happ (happ (happ _1 P) f) x) y <=> happ (happ P (happ f x)) y) ==> (!_0. (!P f x. happ (happ (happ _0 P) f) x = happ (happ (happ _1 P) f) x) ==> (!l2 l1 f P. 'h4/const/list/LIST_REL' P ('h4/const/list/MAP' f l1) l2 <=> 'h4/const/list/LIST_REL' (happ (happ _0 P) f) 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_3f12369,V_3f12365]: ![F, G]: (![X]: s(V_3f12365,happ(s(fun(V_3f12369,V_3f12365),F),s(V_3f12369,X))) = s(V_3f12365,happ(s(fun(V_3f12369,V_3f12365),G),s(V_3f12369,X))) => s(fun(V_3f12369,V_3f12365),F) = s(fun(V_3f12369,V_3f12365),G))).
fof('h4/thm/list/EVERY2_MAP_0', conjecture, ![A,C,B]: ![V__1]: (![P, F, X, Y]: s(bool,happ(s(fun(B,bool),happ(s(fun(C,fun(B,bool)),happ(s(fun(fun(C,A),fun(C,fun(B,bool))),happ(s(fun(fun(A,fun(B,bool)),fun(fun(C,A),fun(C,fun(B,bool)))),V__1),s(fun(A,fun(B,bool)),P))),s(fun(C,A),F))),s(C,X))),s(B,Y))) = s(bool,happ(s(fun(B,bool),happ(s(fun(A,fun(B,bool)),P),s(A,happ(s(fun(C,A),F),s(C,X))))),s(B,Y))) => ![V__0]: (![P, F, X]: s(fun(B,bool),happ(s(fun(C,fun(B,bool)),happ(s(fun(fun(C,A),fun(C,fun(B,bool))),happ(s(fun(fun(A,fun(B,bool)),fun(fun(C,A),fun(C,fun(B,bool)))),V__0),s(fun(A,fun(B,bool)),P))),s(fun(C,A),F))),s(C,X))) = s(fun(B,bool),happ(s(fun(C,fun(B,bool)),happ(s(fun(fun(C,A),fun(C,fun(B,bool))),happ(s(fun(fun(A,fun(B,bool)),fun(fun(C,A),fun(C,fun(B,bool)))),V__1),s(fun(A,fun(B,bool)),P))),s(fun(C,A),F))),s(C,X))) => ![L2, L1, F, P]: s(bool,'h4/const/list/LIST_REL'(s(fun(A,fun(B,bool)),P),s('h4/type/list/list'(A),'h4/const/list/MAP'(s(fun(C,A),F),s('h4/type/list/list'(C),L1))),s('h4/type/list/list'(B),L2))) = s(bool,'h4/const/list/LIST_REL'(s(fun(C,fun(B,bool)),happ(s(fun(fun(C,A),fun(C,fun(B,bool))),happ(s(fun(fun(A,fun(B,bool)),fun(fun(C,A),fun(C,fun(B,bool)))),V__0),s(fun(A,fun(B,bool)),P))),s(fun(C,A),F))),s('h4/type/list/list'(C),L1),s('h4/type/list/list'(B),L2)))))).
