%   ORIGINAL: 'h4/thm/list/SUM_MAP_PLUS_ZIP_'
% 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: !h g f ls1 ls2. 'h4/const/list/LENGTH' ls1 = 'h4/const/list/LENGTH' ls2 /\ (!x y. f ('h4/const/pair/,' x y) = 'h4/const/arithmetic/+' (g x) (h y)) ==> 'h4/const/list/SUM' ('h4/const/list/MAP' f ('h4/const/list/ZIP' ('h4/const/pair/,' ls1 ls2))) = 'h4/const/arithmetic/+' ('h4/const/list/SUM' ('h4/const/list/MAP' g ls1)) ('h4/const/list/SUM' ('h4/const/list/MAP' h ls2))
%   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: !h g f ls1 ls2. 'h4/const/list/LENGTH' ls1 = 'h4/const/list/LENGTH' ls2 /\ (!x y. happ f ('h4/const/pair/,' x y) = 'h4/const/arithmetic/+' (happ g x) (happ h y)) ==> 'h4/const/list/SUM' ('h4/const/list/MAP' f ('h4/const/list/ZIP' ('h4/const/pair/,' ls1 ls2))) = 'h4/const/arithmetic/+' ('h4/const/list/SUM' ('h4/const/list/MAP' g ls1)) ('h4/const/list/SUM' ('h4/const/list/MAP' h ls2))
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_3f6539,V_3f6535]: ![F, G]: (![X]: s(V_3f6535,happ(s(fun(V_3f6539,V_3f6535),F),s(V_3f6539,X))) = s(V_3f6535,happ(s(fun(V_3f6539,V_3f6535),G),s(V_3f6539,X))) => s(fun(V_3f6539,V_3f6535),F) = s(fun(V_3f6539,V_3f6535),G))).
fof('h4/thm/list/SUM_MAP_PLUS_ZIP_', conjecture, ![A,B]: ![H, G, F, Ls1, Ls2]: ((s('h4/type/num/num','h4/const/list/LENGTH'(s('h4/type/list/list'(A),Ls1))) = s('h4/type/num/num','h4/const/list/LENGTH'(s('h4/type/list/list'(B),Ls2))) & ![X, Y]: s('h4/type/num/num',happ(s(fun('h4/type/pair/prod'(A,B),'h4/type/num/num'),F),s('h4/type/pair/prod'(A,B),'h4/const/pair/,'(s(A,X),s(B,Y))))) = s('h4/type/num/num','h4/const/arithmetic/+'(s('h4/type/num/num',happ(s(fun(A,'h4/type/num/num'),G),s(A,X))),s('h4/type/num/num',happ(s(fun(B,'h4/type/num/num'),H),s(B,Y)))))) => s('h4/type/num/num','h4/const/list/SUM'(s('h4/type/list/list'('h4/type/num/num'),'h4/const/list/MAP'(s(fun('h4/type/pair/prod'(A,B),'h4/type/num/num'),F),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),Ls1),s('h4/type/list/list'(B),Ls2))))))))) = 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'),G),s('h4/type/list/list'(A),Ls1))))),s('h4/type/num/num','h4/const/list/SUM'(s('h4/type/list/list'('h4/type/num/num'),'h4/const/list/MAP'(s(fun(B,'h4/type/num/num'),H),s('h4/type/list/list'(B),Ls2))))))))).
