%   ORIGINAL: 'h4/thm/list/LIST_REL_MAP1_'
% 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' R ('h4/const/list/MAP' f l1) l2 <=> 'h4/const/list/LIST_REL' ('h4/const/combin/o' R f) 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: !l2 l1 f R. 'h4/const/list/LIST_REL' R ('h4/const/list/MAP' f l1) l2 <=> 'h4/const/list/LIST_REL' ('h4/const/combin/o' 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_3f5889,V_3f5885]: ![F, G]: (![X]: s(V_3f5885,happ(s(fun(V_3f5889,V_3f5885),F),s(V_3f5889,X))) = s(V_3f5885,happ(s(fun(V_3f5889,V_3f5885),G),s(V_3f5889,X))) => s(fun(V_3f5889,V_3f5885),F) = s(fun(V_3f5889,V_3f5885),G))).
fof('h4/thm/list/LIST_REL_MAP1_', conjecture, ![A,C,B]: ![L2, L1, F, R]: s(bool,'h4/const/list/LIST_REL'(s(fun(A,fun(B,bool)),R),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)),'h4/const/combin/o'(s(fun(A,fun(B,bool)),R),s(fun(C,A),F))),s('h4/type/list/list'(C),L1),s('h4/type/list/list'(B),L2)))).
