%   ORIGINAL: 'h4/thm/list/EVERY2_MAP_e1'
% 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 g Q. 'h4/const/list/LIST_REL' Q l1 ('h4/const/list/MAP' g l2) <=> 'h4/const/list/LIST_REL' (\x y. Q x (g 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. (!Q x g y. happ (happ (happ (happ _1 Q) x) g) y <=> happ (happ Q x) (happ g y)) ==> (!_0. (!Q g x. happ (happ (happ _0 Q) g) x = happ (happ (happ _1 Q) x) g) ==> (!l2 l1 g Q. 'h4/const/list/LIST_REL' Q l1 ('h4/const/list/MAP' g l2) <=> 'h4/const/list/LIST_REL' (happ (happ _0 Q) g) 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_3f12394,V_3f12390]: ![F, G]: (![X]: s(V_3f12390,happ(s(fun(V_3f12394,V_3f12390),F),s(V_3f12394,X))) = s(V_3f12390,happ(s(fun(V_3f12394,V_3f12390),G),s(V_3f12394,X))) => s(fun(V_3f12394,V_3f12390),F) = s(fun(V_3f12394,V_3f12390),G))).
fof('h4/thm/list/EVERY2_MAP_e1', conjecture, ![D,C,B]: ![V__1]: (![Q, X, G, Y]: s(bool,happ(s(fun(B,bool),happ(s(fun(fun(B,D),fun(B,bool)),happ(s(fun(C,fun(fun(B,D),fun(B,bool))),happ(s(fun(fun(C,fun(D,bool)),fun(C,fun(fun(B,D),fun(B,bool)))),V__1),s(fun(C,fun(D,bool)),Q))),s(C,X))),s(fun(B,D),G))),s(B,Y))) = s(bool,happ(s(fun(D,bool),happ(s(fun(C,fun(D,bool)),Q),s(C,X))),s(D,happ(s(fun(B,D),G),s(B,Y))))) => ![V__0]: (![Q, G, X]: s(fun(B,bool),happ(s(fun(C,fun(B,bool)),happ(s(fun(fun(B,D),fun(C,fun(B,bool))),happ(s(fun(fun(C,fun(D,bool)),fun(fun(B,D),fun(C,fun(B,bool)))),V__0),s(fun(C,fun(D,bool)),Q))),s(fun(B,D),G))),s(C,X))) = s(fun(B,bool),happ(s(fun(fun(B,D),fun(B,bool)),happ(s(fun(C,fun(fun(B,D),fun(B,bool))),happ(s(fun(fun(C,fun(D,bool)),fun(C,fun(fun(B,D),fun(B,bool)))),V__1),s(fun(C,fun(D,bool)),Q))),s(C,X))),s(fun(B,D),G))) => ![L2, L1, G, Q]: s(bool,'h4/const/list/LIST_REL'(s(fun(C,fun(D,bool)),Q),s('h4/type/list/list'(C),L1),s('h4/type/list/list'(D),'h4/const/list/MAP'(s(fun(B,D),G),s('h4/type/list/list'(B),L2))))) = s(bool,'h4/const/list/LIST_REL'(s(fun(C,fun(B,bool)),happ(s(fun(fun(B,D),fun(C,fun(B,bool))),happ(s(fun(fun(C,fun(D,bool)),fun(fun(B,D),fun(C,fun(B,bool)))),V__0),s(fun(C,fun(D,bool)),Q))),s(fun(B,D),G))),s('h4/type/list/list'(C),L1),s('h4/type/list/list'(B),L2)))))).
