%   ORIGINAL: 'h4/thm/list/LIST_REL_MAP2_'
% 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 R. 'h4/const/list/LIST_REL' (\a b. R a b) l1 ('h4/const/list/MAP' f l2) <=> 'h4/const/list/LIST_REL' (\a b. R a (f b)) 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: !_3. (!R a f b. happ (happ (happ (happ _3 R) a) f) b <=> happ (happ R a) (happ f b)) ==> (!_2. (!R f a. happ (happ (happ _2 R) f) a = happ (happ (happ _3 R) a) f) ==> (!_1. (!R a b. happ (happ (happ _1 R) a) b <=> happ (happ R a) b) ==> (!_0. (!R a. happ (happ _0 R) a = happ (happ _1 R) a) ==> (!l2 l1 f R. 'h4/const/list/LIST_REL' (happ _0 R) l1 ('h4/const/list/MAP' f l2) <=> 'h4/const/list/LIST_REL' (happ (happ _2 R) 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_3f5914,V_3f5910]: ![F, G]: (![X]: s(V_3f5910,happ(s(fun(V_3f5914,V_3f5910),F),s(V_3f5914,X))) = s(V_3f5910,happ(s(fun(V_3f5914,V_3f5910),G),s(V_3f5914,X))) => s(fun(V_3f5914,V_3f5910),F) = s(fun(V_3f5914,V_3f5910),G))).
fof('h4/thm/list/LIST_REL_MAP2_', conjecture, ![B,A,C]: ![V__3]: (![R, A0, F, B0]: 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,fun(B,bool)),fun(A,fun(fun(C,B),fun(C,bool)))),V__3),s(fun(A,fun(B,bool)),R))),s(A,A0))),s(fun(C,B),F))),s(C,B0))) = s(bool,happ(s(fun(B,bool),happ(s(fun(A,fun(B,bool)),R),s(A,A0))),s(B,happ(s(fun(C,B),F),s(C,B0))))) => ![V__2]: (![R, F, A0]: 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,fun(B,bool)),fun(fun(C,B),fun(A,fun(C,bool)))),V__2),s(fun(A,fun(B,bool)),R))),s(fun(C,B),F))),s(A,A0))) = 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,fun(B,bool)),fun(A,fun(fun(C,B),fun(C,bool)))),V__3),s(fun(A,fun(B,bool)),R))),s(A,A0))),s(fun(C,B),F))) => ![V__1]: (![R, A0, B0]: s(bool,happ(s(fun(B,bool),happ(s(fun(A,fun(B,bool)),happ(s(fun(fun(A,fun(B,bool)),fun(A,fun(B,bool))),V__1),s(fun(A,fun(B,bool)),R))),s(A,A0))),s(B,B0))) = s(bool,happ(s(fun(B,bool),happ(s(fun(A,fun(B,bool)),R),s(A,A0))),s(B,B0))) => ![V__0]: (![R, A0]: s(fun(B,bool),happ(s(fun(A,fun(B,bool)),happ(s(fun(fun(A,fun(B,bool)),fun(A,fun(B,bool))),V__0),s(fun(A,fun(B,bool)),R))),s(A,A0))) = s(fun(B,bool),happ(s(fun(A,fun(B,bool)),happ(s(fun(fun(A,fun(B,bool)),fun(A,fun(B,bool))),V__1),s(fun(A,fun(B,bool)),R))),s(A,A0))) => ![L2, L1, F, R]: s(bool,'h4/const/list/LIST_REL'(s(fun(A,fun(B,bool)),happ(s(fun(fun(A,fun(B,bool)),fun(A,fun(B,bool))),V__0),s(fun(A,fun(B,bool)),R))),s('h4/type/list/list'(A),L1),s('h4/type/list/list'(B),'h4/const/list/MAP'(s(fun(C,B),F),s('h4/type/list/list'(C),L2))))) = 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,fun(B,bool)),fun(fun(C,B),fun(A,fun(C,bool)))),V__2),s(fun(A,fun(B,bool)),R))),s(fun(C,B),F))),s('h4/type/list/list'(A),L1),s('h4/type/list/list'(C),L2)))))))).
