%   ORIGINAL: 'h4/thm/list/SUM_MAP_PLUS_'
% 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 g ls. 'h4/const/list/SUM' ('h4/const/list/MAP' (\x. 'h4/const/arithmetic/+' (f x) (g x)) ls) = 'h4/const/arithmetic/+' ('h4/const/list/SUM' ('h4/const/list/MAP' f ls)) ('h4/const/list/SUM' ('h4/const/list/MAP' g 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 g x. happ (happ (happ _0 f) g) x = 'h4/const/arithmetic/+' (happ f x) (happ g x)) ==> (!f g ls. 'h4/const/list/SUM' ('h4/const/list/MAP' (happ (happ _0 f) g) ls) = 'h4/const/arithmetic/+' ('h4/const/list/SUM' ('h4/const/list/MAP' f ls)) ('h4/const/list/SUM' ('h4/const/list/MAP' g 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_3f11594,V_3f11590]: ![F, G]: (![X]: s(V_3f11590,happ(s(fun(V_3f11594,V_3f11590),F),s(V_3f11594,X))) = s(V_3f11590,happ(s(fun(V_3f11594,V_3f11590),G),s(V_3f11594,X))) => s(fun(V_3f11594,V_3f11590),F) = s(fun(V_3f11594,V_3f11590),G))).
fof('h4/thm/list/SUM_MAP_PLUS_', conjecture, ![A]: ![V__0]: (![F, G, X]: 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(fun(A,'h4/type/num/num'),fun(fun(A,'h4/type/num/num'),fun(A,'h4/type/num/num'))),V__0),s(fun(A,'h4/type/num/num'),F))),s(fun(A,'h4/type/num/num'),G))),s(A,X))) = s('h4/type/num/num','h4/const/arithmetic/+'(s('h4/type/num/num',happ(s(fun(A,'h4/type/num/num'),F),s(A,X))),s('h4/type/num/num',happ(s(fun(A,'h4/type/num/num'),G),s(A,X))))) => ![F, G, 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'),happ(s(fun(fun(A,'h4/type/num/num'),fun(A,'h4/type/num/num')),happ(s(fun(fun(A,'h4/type/num/num'),fun(fun(A,'h4/type/num/num'),fun(A,'h4/type/num/num'))),V__0),s(fun(A,'h4/type/num/num'),F))),s(fun(A,'h4/type/num/num'),G))),s('h4/type/list/list'(A),Ls))))) = s('h4/type/num/num','h4/const/arithmetic/+'(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/SUM'(s('h4/type/list/list'('h4/type/num/num'),'h4/const/list/MAP'(s(fun(A,'h4/type/num/num'),G),s('h4/type/list/list'(A),Ls))))))))).
