%   ORIGINAL: 'h4/thm/real/REAL_SUB_0_'
% 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 y. 'h4/const/real/real_sub' x y = 'h4/const/real/real_of_num' 'h4/const/num/0' <=> 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: !x y. 'h4/const/real/real_sub' x y = 'h4/const/real/real_of_num' 'h4/const/num/0' <=> 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_3f89269,V_3f89265]: ![F, G]: (![X]: s(V_3f89265,happ(s(fun(V_3f89269,V_3f89265),F),s(V_3f89269,X))) = s(V_3f89265,happ(s(fun(V_3f89269,V_3f89265),G),s(V_3f89269,X))) => s(fun(V_3f89269,V_3f89265),F) = s(fun(V_3f89269,V_3f89265),G))).
fof('h4/thm/real/REAL_SUB_0_', conjecture, ![X, Y]: (s('h4/type/realax/real','h4/const/real/real_sub'(s('h4/type/realax/real',X),s('h4/type/realax/real',Y))) = s('h4/type/realax/real','h4/const/real/real_of_num'(s('h4/type/num/num','h4/const/num/0'))) <=> s('h4/type/realax/real',X) = s('h4/type/realax/real',Y))).
