%   ORIGINAL: 'h4/thm/sum/FORALL_SUM_'
% 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: !P. (!s. P s) <=> (!x. P ('h4/const/sum/INL' x)) /\ (!y. P ('h4/const/sum/INR' y))
%   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: !P. (!s. happ P s) <=> (!x. happ P ('h4/const/sum/INL' x)) /\ (!y. happ P ('h4/const/sum/INR' y))
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_3f66161,V_3f66157]: ![F, G]: (![X]: s(V_3f66157,happ(s(fun(V_3f66161,V_3f66157),F),s(V_3f66161,X))) = s(V_3f66157,happ(s(fun(V_3f66161,V_3f66157),G),s(V_3f66161,X))) => s(fun(V_3f66161,V_3f66157),F) = s(fun(V_3f66161,V_3f66157),G))).
fof('h4/thm/sum/FORALL_SUM_', conjecture, ![A,B]: ![P]: (![S]: p(s(bool,happ(s(fun('h4/type/sum/sum'(A,B),bool),P),s('h4/type/sum/sum'(A,B),S)))) <=> (![X]: p(s(bool,happ(s(fun('h4/type/sum/sum'(A,B),bool),P),s('h4/type/sum/sum'(A,B),'h4/const/sum/INL'(s(A,X)))))) & ![Y]: p(s(bool,happ(s(fun('h4/type/sum/sum'(A,B),bool),P),s('h4/type/sum/sum'(A,B),'h4/const/sum/INR'(s(B,Y))))))))).
