%   ORIGINAL: 'h4/thm/bool/UEXISTS_SIMP_'
% 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: !t. 'h4/const/bool/?!' (\x. t) <=> t /\ (!x y. x = 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: !_0. (!t x. happ (happ _0 t) x <=> t) ==> (!t. 'h4/const/bool/?!' (happ _0 t) <=> t /\ (!x y. x = 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_3f35153,V_3f35149]: ![F, G]: (![X]: s(V_3f35149,happ(s(fun(V_3f35153,V_3f35149),F),s(V_3f35153,X))) = s(V_3f35149,happ(s(fun(V_3f35153,V_3f35149),G),s(V_3f35153,X))) => s(fun(V_3f35153,V_3f35149),F) = s(fun(V_3f35153,V_3f35149),G))).
fof('h4/thm/bool/UEXISTS_SIMP_', conjecture, ![A]: ![V__0]: (![T, X]: s(bool,happ(s(fun(A,bool),happ(s(fun(bool,fun(A,bool)),V__0),s(bool,T))),s(A,X))) = s(bool,T) => ![T]: (p(s(bool,'h4/const/bool/?!'(s(fun(A,bool),happ(s(fun(bool,fun(A,bool)),V__0),s(bool,T)))))) <=> (p(s(bool,T)) & ![X, Y]: s(A,X) = s(A,Y))))).
