%   ORIGINAL: 'h4/thm/list/MAP_ZIP_SAME_'
% 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: !ls f. 'h4/const/list/MAP' f ('h4/const/list/ZIP' ('h4/const/pair/,' ls ls)) = 'h4/const/list/MAP' (\x. f ('h4/const/pair/,' x x)) ls
%   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: !_0. (!f x. happ (happ _0 f) x = happ f ('h4/const/pair/,' x x)) ==> (!ls f. 'h4/const/list/MAP' f ('h4/const/list/ZIP' ('h4/const/pair/,' ls ls)) = 'h4/const/list/MAP' (happ _0 f) ls)
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_3f9916,V_3f9912]: ![F, G]: (![X]: s(V_3f9912,happ(s(fun(V_3f9916,V_3f9912),F),s(V_3f9916,X))) = s(V_3f9912,happ(s(fun(V_3f9916,V_3f9912),G),s(V_3f9916,X))) => s(fun(V_3f9916,V_3f9912),F) = s(fun(V_3f9916,V_3f9912),G))).
fof('h4/thm/list/MAP_ZIP_SAME_', conjecture, ![B,A]: ![V__0]: (![F, X]: s(B,happ(s(fun(A,B),happ(s(fun(fun('h4/type/pair/prod'(A,A),B),fun(A,B)),V__0),s(fun('h4/type/pair/prod'(A,A),B),F))),s(A,X))) = s(B,happ(s(fun('h4/type/pair/prod'(A,A),B),F),s('h4/type/pair/prod'(A,A),'h4/const/pair/,'(s(A,X),s(A,X))))) => ![Ls, F]: s('h4/type/list/list'(B),'h4/const/list/MAP'(s(fun('h4/type/pair/prod'(A,A),B),F),s('h4/type/list/list'('h4/type/pair/prod'(A,A)),'h4/const/list/ZIP'(s('h4/type/pair/prod'('h4/type/list/list'(A),'h4/type/list/list'(A)),'h4/const/pair/,'(s('h4/type/list/list'(A),Ls),s('h4/type/list/list'(A),Ls))))))) = s('h4/type/list/list'(B),'h4/const/list/MAP'(s(fun(A,B),happ(s(fun(fun('h4/type/pair/prod'(A,A),B),fun(A,B)),V__0),s(fun('h4/type/pair/prod'(A,A),B),F))),s('h4/type/list/list'(A),Ls))))).
