%   ORIGINAL: 'h4/thm/list/FOLDL_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 e. 'h4/const/list/FOLDL' f e ('h4/const/list/ZIP' ('h4/const/pair/,' ls ls)) = 'h4/const/list/FOLDL' (\x y. f x ('h4/const/pair/,' y y)) e 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: !_1. (!f x y. happ (happ (happ _1 f) x) y = happ (happ f x) ('h4/const/pair/,' y y)) ==> (!_0. (!f x. happ (happ _0 f) x = happ (happ _1 f) x) ==> (!ls f e. 'h4/const/list/FOLDL' f e ('h4/const/list/ZIP' ('h4/const/pair/,' ls ls)) = 'h4/const/list/FOLDL' (happ _0 f) e 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_3f9891,V_3f9887]: ![F, G]: (![X]: s(V_3f9887,happ(s(fun(V_3f9891,V_3f9887),F),s(V_3f9891,X))) = s(V_3f9887,happ(s(fun(V_3f9891,V_3f9887),G),s(V_3f9891,X))) => s(fun(V_3f9891,V_3f9887),F) = s(fun(V_3f9891,V_3f9887),G))).
fof('h4/thm/list/FOLDL_ZIP_SAME_', conjecture, ![B,A]: ![V__1]: (![F, X, Y]: s(B,happ(s(fun(A,B),happ(s(fun(B,fun(A,B)),happ(s(fun(fun(B,fun('h4/type/pair/prod'(A,A),B)),fun(B,fun(A,B))),V__1),s(fun(B,fun('h4/type/pair/prod'(A,A),B)),F))),s(B,X))),s(A,Y))) = s(B,happ(s(fun('h4/type/pair/prod'(A,A),B),happ(s(fun(B,fun('h4/type/pair/prod'(A,A),B)),F),s(B,X))),s('h4/type/pair/prod'(A,A),'h4/const/pair/,'(s(A,Y),s(A,Y))))) => ![V__0]: (![F, X]: s(fun(A,B),happ(s(fun(B,fun(A,B)),happ(s(fun(fun(B,fun('h4/type/pair/prod'(A,A),B)),fun(B,fun(A,B))),V__0),s(fun(B,fun('h4/type/pair/prod'(A,A),B)),F))),s(B,X))) = s(fun(A,B),happ(s(fun(B,fun(A,B)),happ(s(fun(fun(B,fun('h4/type/pair/prod'(A,A),B)),fun(B,fun(A,B))),V__1),s(fun(B,fun('h4/type/pair/prod'(A,A),B)),F))),s(B,X))) => ![Ls, F, E]: s(B,'h4/const/list/FOLDL'(s(fun(B,fun('h4/type/pair/prod'(A,A),B)),F),s(B,E),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(B,'h4/const/list/FOLDL'(s(fun(B,fun(A,B)),happ(s(fun(fun(B,fun('h4/type/pair/prod'(A,A),B)),fun(B,fun(A,B))),V__0),s(fun(B,fun('h4/type/pair/prod'(A,A),B)),F))),s(B,E),s('h4/type/list/list'(A),Ls)))))).
