%   ORIGINAL: 'h4/thm/list/MAP2_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: !f h1 t1 h2 t2. 'h4/const/list/MAP2' f ('h4/const/list/CONS' h1 t1) ('h4/const/list/CONS' h2 t2) = 'h4/const/list/CONS' (f h1 h2) ('h4/const/list/MAP2' f t1 t2)
%   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: !f h1 t1 h2 t2. 'h4/const/list/MAP2' f ('h4/const/list/CONS' h1 t1) ('h4/const/list/CONS' h2 t2) = 'h4/const/list/CONS' (happ (happ f h1) h2) ('h4/const/list/MAP2' f t1 t2)
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_3f2738,V_3f2734]: ![F0, G]: (![X]: s(V_3f2734,happ(s(fun(V_3f2738,V_3f2734),F0),s(V_3f2738,X))) = s(V_3f2734,happ(s(fun(V_3f2738,V_3f2734),G),s(V_3f2738,X))) => s(fun(V_3f2738,V_3f2734),F0) = s(fun(V_3f2738,V_3f2734),G))).
fof('h4/thm/list/MAP2_e1', conjecture, ![F,D,E]: ![F0, H1, T1, H2, T2]: s('h4/type/list/list'(F),'h4/const/list/MAP2'(s(fun(D,fun(E,F)),F0),s('h4/type/list/list'(D),'h4/const/list/CONS'(s(D,H1),s('h4/type/list/list'(D),T1))),s('h4/type/list/list'(E),'h4/const/list/CONS'(s(E,H2),s('h4/type/list/list'(E),T2))))) = s('h4/type/list/list'(F),'h4/const/list/CONS'(s(F,happ(s(fun(E,F),happ(s(fun(D,fun(E,F)),F0),s(D,H1))),s(E,H2))),s('h4/type/list/list'(F),'h4/const/list/MAP2'(s(fun(D,fun(E,F)),F0),s('h4/type/list/list'(D),T1),s('h4/type/list/list'(E),T2)))))).
