%   ORIGINAL: 'h4/thm/list/FOLDL2_FOLDL_'
% 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: !l1 l2. 'h4/const/list/LENGTH' l1 = 'h4/const/list/LENGTH' l2 ==> (!f a. 'h4/const/list/FOLDL2' f a l1 l2 = 'h4/const/list/FOLDL' (\a0. 'h4/const/pair/UNCURRY' (f a0)) a ('h4/const/list/ZIP' ('h4/const/pair/,' 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: !_0. (!f a0. happ (happ _0 f) a0 = 'h4/const/pair/UNCURRY' (happ f a0)) ==> (!l1 l2. 'h4/const/list/LENGTH' l1 = 'h4/const/list/LENGTH' l2 ==> (!f a. 'h4/const/list/FOLDL2' f a l1 l2 = 'h4/const/list/FOLDL' (happ _0 f) a ('h4/const/list/ZIP' ('h4/const/pair/,' 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_3f7465,V_3f7461]: ![F, G]: (![X]: s(V_3f7461,happ(s(fun(V_3f7465,V_3f7461),F),s(V_3f7465,X))) = s(V_3f7461,happ(s(fun(V_3f7465,V_3f7461),G),s(V_3f7465,X))) => s(fun(V_3f7465,V_3f7461),F) = s(fun(V_3f7465,V_3f7461),G))).
fof('h4/thm/list/FOLDL2_FOLDL_', conjecture, ![C,A,B]: ![V__0]: (![F, A0]: s(fun('h4/type/pair/prod'(A,B),C),happ(s(fun(C,fun('h4/type/pair/prod'(A,B),C)),happ(s(fun(fun(C,fun(A,fun(B,C))),fun(C,fun('h4/type/pair/prod'(A,B),C))),V__0),s(fun(C,fun(A,fun(B,C))),F))),s(C,A0))) = s(fun('h4/type/pair/prod'(A,B),C),'h4/const/pair/UNCURRY'(s(fun(A,fun(B,C)),happ(s(fun(C,fun(A,fun(B,C))),F),s(C,A0))))) => ![L1, L2]: (s('h4/type/num/num','h4/const/list/LENGTH'(s('h4/type/list/list'(A),L1))) = s('h4/type/num/num','h4/const/list/LENGTH'(s('h4/type/list/list'(B),L2))) => ![F, A0]: s(C,'h4/const/list/FOLDL2'(s(fun(C,fun(A,fun(B,C))),F),s(C,A0),s('h4/type/list/list'(A),L1),s('h4/type/list/list'(B),L2))) = s(C,'h4/const/list/FOLDL'(s(fun(C,fun('h4/type/pair/prod'(A,B),C)),happ(s(fun(fun(C,fun(A,fun(B,C))),fun(C,fun('h4/type/pair/prod'(A,B),C))),V__0),s(fun(C,fun(A,fun(B,C))),F))),s(C,A0),s('h4/type/list/list'('h4/type/pair/prod'(A,B)),'h4/const/list/ZIP'(s('h4/type/pair/prod'('h4/type/list/list'(A),'h4/type/list/list'(B)),'h4/const/pair/,'(s('h4/type/list/list'(A),L1),s('h4/type/list/list'(B),L2)))))))))).
