%   ORIGINAL: 'h4/thm/list/MAP2_def_e2'
% 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: !v5 v4 f. 'h4/const/list/MAP2' f ('h4/const/list/CONS' v4 v5) 'h4/const/list/NIL' = 'h4/const/list/NIL'
%   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: !v5 v4 f. 'h4/const/list/MAP2' f ('h4/const/list/CONS' v4 v5) 'h4/const/list/NIL' = 'h4/const/list/NIL'
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_3f2688,V_3f2684]: ![F, G]: (![X]: s(V_3f2684,happ(s(fun(V_3f2688,V_3f2684),F),s(V_3f2688,X))) = s(V_3f2684,happ(s(fun(V_3f2688,V_3f2684),G),s(V_3f2688,X))) => s(fun(V_3f2688,V_3f2684),F) = s(fun(V_3f2688,V_3f2684),G))).
fof('h4/thm/list/MAP2_def_e2', conjecture, ![B,C,A]: ![V5, V4, F]: s('h4/type/list/list'(A),'h4/const/list/MAP2'(s(fun(B,fun(C,A)),F),s('h4/type/list/list'(B),'h4/const/list/CONS'(s(B,V4),s('h4/type/list/list'(B),V5))),s('h4/type/list/list'(C),'h4/const/list/NIL'))) = s('h4/type/list/list'(A),'h4/const/list/NIL')).
