%   ORIGINAL: 'h4/thm/bool/UEXISTS_OR_THM_'
% 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 Q. 'h4/const/bool/?!' (\x. P x \/ Q x) ==> 'h4/const/bool/?!' (\x. P x) \/ 'h4/const/bool/?!' (\x. Q x)
%   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. (!P x. happ (happ _1 P) x <=> happ P x) ==> (!_0. (!P Q x. happ (happ (happ _0 P) Q) x <=> happ P x \/ happ Q x) ==> (!P Q. 'h4/const/bool/?!' (happ (happ _0 P) Q) ==> 'h4/const/bool/?!' (happ _1 P) \/ 'h4/const/bool/?!' (happ _1 Q)))
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_3f35128,V_3f35124]: ![F, G]: (![X]: s(V_3f35124,happ(s(fun(V_3f35128,V_3f35124),F),s(V_3f35128,X))) = s(V_3f35124,happ(s(fun(V_3f35128,V_3f35124),G),s(V_3f35128,X))) => s(fun(V_3f35128,V_3f35124),F) = s(fun(V_3f35128,V_3f35124),G))).
fof('h4/thm/bool/UEXISTS_OR_THM_', conjecture, ![A]: ![V__1]: (![P, X]: s(bool,happ(s(fun(A,bool),happ(s(fun(fun(A,bool),fun(A,bool)),V__1),s(fun(A,bool),P))),s(A,X))) = s(bool,happ(s(fun(A,bool),P),s(A,X))) => ![V__0]: (![P, Q, X]: (p(s(bool,happ(s(fun(A,bool),happ(s(fun(fun(A,bool),fun(A,bool)),happ(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),V__0),s(fun(A,bool),P))),s(fun(A,bool),Q))),s(A,X)))) <=> (p(s(bool,happ(s(fun(A,bool),P),s(A,X)))) | p(s(bool,happ(s(fun(A,bool),Q),s(A,X)))))) => ![P, Q]: (p(s(bool,'h4/const/bool/?!'(s(fun(A,bool),happ(s(fun(fun(A,bool),fun(A,bool)),happ(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),V__0),s(fun(A,bool),P))),s(fun(A,bool),Q)))))) => (p(s(bool,'h4/const/bool/?!'(s(fun(A,bool),happ(s(fun(fun(A,bool),fun(A,bool)),V__1),s(fun(A,bool),P)))))) | p(s(bool,'h4/const/bool/?!'(s(fun(A,bool),happ(s(fun(fun(A,bool),fun(A,bool)),V__1),s(fun(A,bool),Q))))))))))).
