%   ORIGINAL: 'h4/thm/list/SUM_MAP_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: !f ls. 'h4/const/list/SUM' ('h4/const/list/MAP' f ls) = 'h4/const/list/FOLDL' (\a e. 'h4/const/arithmetic/+' a (f e)) 'h4/const/num/0' 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. (!a f e. happ (happ (happ _1 a) f) e = 'h4/const/arithmetic/+' a (happ f e)) ==> (!_0. (!f a. happ (happ _0 f) a = happ (happ _1 a) f) ==> (!f ls. 'h4/const/list/SUM' ('h4/const/list/MAP' f ls) = 'h4/const/list/FOLDL' (happ _0 f) 'h4/const/num/0' 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_3f9741,V_3f9737]: ![F, G]: (![X]: s(V_3f9737,happ(s(fun(V_3f9741,V_3f9737),F),s(V_3f9741,X))) = s(V_3f9737,happ(s(fun(V_3f9741,V_3f9737),G),s(V_3f9741,X))) => s(fun(V_3f9741,V_3f9737),F) = s(fun(V_3f9741,V_3f9737),G))).
fof('h4/thm/list/SUM_MAP_FOLDL_', conjecture, ![A]: ![V__1]: (![A0, F, E]: s('h4/type/num/num',happ(s(fun(A,'h4/type/num/num'),happ(s(fun(fun(A,'h4/type/num/num'),fun(A,'h4/type/num/num')),happ(s(fun('h4/type/num/num',fun(fun(A,'h4/type/num/num'),fun(A,'h4/type/num/num'))),V__1),s('h4/type/num/num',A0))),s(fun(A,'h4/type/num/num'),F))),s(A,E))) = s('h4/type/num/num','h4/const/arithmetic/+'(s('h4/type/num/num',A0),s('h4/type/num/num',happ(s(fun(A,'h4/type/num/num'),F),s(A,E))))) => ![V__0]: (![F, A0]: s(fun(A,'h4/type/num/num'),happ(s(fun('h4/type/num/num',fun(A,'h4/type/num/num')),happ(s(fun(fun(A,'h4/type/num/num'),fun('h4/type/num/num',fun(A,'h4/type/num/num'))),V__0),s(fun(A,'h4/type/num/num'),F))),s('h4/type/num/num',A0))) = s(fun(A,'h4/type/num/num'),happ(s(fun(fun(A,'h4/type/num/num'),fun(A,'h4/type/num/num')),happ(s(fun('h4/type/num/num',fun(fun(A,'h4/type/num/num'),fun(A,'h4/type/num/num'))),V__1),s('h4/type/num/num',A0))),s(fun(A,'h4/type/num/num'),F))) => ![F, Ls]: s('h4/type/num/num','h4/const/list/SUM'(s('h4/type/list/list'('h4/type/num/num'),'h4/const/list/MAP'(s(fun(A,'h4/type/num/num'),F),s('h4/type/list/list'(A),Ls))))) = s('h4/type/num/num','h4/const/list/FOLDL'(s(fun('h4/type/num/num',fun(A,'h4/type/num/num')),happ(s(fun(fun(A,'h4/type/num/num'),fun('h4/type/num/num',fun(A,'h4/type/num/num'))),V__0),s(fun(A,'h4/type/num/num'),F))),s('h4/type/num/num','h4/const/num/0'),s('h4/type/list/list'(A),Ls)))))).
