%   ORIGINAL: 'h4/thm/sum/SUM_MAP_CASE_'
% 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 z. 'h4/const/sum/++' f g z = 'h4/const/sum/sum_CASE' z ('h4/const/combin/o' 'h4/const/sum/INL' f) ('h4/const/combin/o' 'h4/const/sum/INR' g)
%   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: !f g z. 'h4/const/sum/++' f g z = 'h4/const/sum/sum_CASE' z ('h4/const/combin/o' 'h4/const/sum/INL' f) ('h4/const/combin/o' 'h4/const/sum/INR' g)
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_3f66436,V_3f66432]: ![F, G]: (![X]: s(V_3f66432,happ(s(fun(V_3f66436,V_3f66432),F),s(V_3f66436,X))) = s(V_3f66432,happ(s(fun(V_3f66436,V_3f66432),G),s(V_3f66436,X))) => s(fun(V_3f66436,V_3f66432),F) = s(fun(V_3f66436,V_3f66432),G))).
fof('h4/thm/sum/SUM_MAP_CASE_', conjecture, ![A,C,B,D]: ![F, G, Z]: s('h4/type/sum/sum'(C,D),'h4/const/sum/++'(s(fun(A,C),F),s(fun(B,D),G),s('h4/type/sum/sum'(A,B),Z))) = s('h4/type/sum/sum'(C,D),'h4/const/sum/sum_CASE'(s('h4/type/sum/sum'(A,B),Z),s(fun(A,'h4/type/sum/sum'(C,D)),'h4/const/combin/o'(s(fun(C,'h4/type/sum/sum'(C,D)),'h4/const/sum/INL'),s(fun(A,C),F))),s(fun(B,'h4/type/sum/sum'(C,D)),'h4/const/combin/o'(s(fun(D,'h4/type/sum/sum'(C,D)),'h4/const/sum/INR'),s(fun(B,D),G)))))).
