%   ORIGINAL: 'h4/thm/real/REAL_SUP_CONST_'
% 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: !x. 'h4/const/real/sup' (\r. r = x) = 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: !_0. (!x r. happ (happ _0 x) r <=> r = x) ==> (!x. 'h4/const/real/sup' (happ _0 x) = x)
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_3f96770,V_3f96766]: ![F, G]: (![X]: s(V_3f96766,happ(s(fun(V_3f96770,V_3f96766),F),s(V_3f96770,X))) = s(V_3f96766,happ(s(fun(V_3f96770,V_3f96766),G),s(V_3f96770,X))) => s(fun(V_3f96770,V_3f96766),F) = s(fun(V_3f96770,V_3f96766),G))).
fof('h4/thm/real/REAL_SUP_CONST_', conjecture, ![V__0]: (![X, R]: (p(s(bool,happ(s(fun('h4/type/realax/real',bool),happ(s(fun('h4/type/realax/real',fun('h4/type/realax/real',bool)),V__0),s('h4/type/realax/real',X))),s('h4/type/realax/real',R)))) <=> s('h4/type/realax/real',R) = s('h4/type/realax/real',X)) => ![X]: s('h4/type/realax/real','h4/const/real/sup'(s(fun('h4/type/realax/real',bool),happ(s(fun('h4/type/realax/real',fun('h4/type/realax/real',bool)),V__0),s('h4/type/realax/real',X))))) = s('h4/type/realax/real',X))).
