%   ORIGINAL: 'h4/thm/res_quan/RES_EXISTS_UNIQUE_ALT_'
% 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 m. 'h4/const/bool/RES_EXISTS_UNIQUE' p m <=> 'h4/const/bool/RES_EXISTS' p (\x. m x /\ 'h4/const/bool/RES_FORALL' p (\y. m y ==> y = 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. (!m x y. happ (happ (happ _1 m) x) y <=> happ m y ==> y = x) ==> (!_0. (!p m x. happ (happ (happ _0 p) m) x <=> happ m x /\ 'h4/const/bool/RES_FORALL' p (happ (happ _1 m) x)) ==> (!p m. 'h4/const/bool/RES_EXISTS_UNIQUE' p m <=> 'h4/const/bool/RES_EXISTS' p (happ (happ _0 p) m)))
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_3f31253,V_3f31249]: ![F, G]: (![X]: s(V_3f31249,happ(s(fun(V_3f31253,V_3f31249),F),s(V_3f31253,X))) = s(V_3f31249,happ(s(fun(V_3f31253,V_3f31249),G),s(V_3f31253,X))) => s(fun(V_3f31253,V_3f31249),F) = s(fun(V_3f31253,V_3f31249),G))).
fof('h4/thm/res_quan/RES_EXISTS_UNIQUE_ALT_', conjecture, ![A]: ![V__1]: (![M, X, Y]: (p(s(bool,happ(s(fun(A,bool),happ(s(fun(A,fun(A,bool)),happ(s(fun(fun(A,bool),fun(A,fun(A,bool))),V__1),s(fun(A,bool),M))),s(A,X))),s(A,Y)))) <=> (p(s(bool,happ(s(fun(A,bool),M),s(A,Y)))) => s(A,Y) = s(A,X))) => ![V__0]: (![P, M, 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),M))),s(A,X)))) <=> (p(s(bool,happ(s(fun(A,bool),M),s(A,X)))) & p(s(bool,'h4/const/bool/RES_FORALL'(s(fun(A,bool),P),s(fun(A,bool),happ(s(fun(A,fun(A,bool)),happ(s(fun(fun(A,bool),fun(A,fun(A,bool))),V__1),s(fun(A,bool),M))),s(A,X)))))))) => ![P, M]: s(bool,'h4/const/bool/RES_EXISTS_UNIQUE'(s(fun(A,bool),P),s(fun(A,bool),M))) = s(bool,'h4/const/bool/RES_EXISTS'(s(fun(A,bool),P),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),M)))))))).
