%   ORIGINAL: 'h4/thm/lim/LIM_X_'
% 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: !x0. 'h4/const/lim/tends_real_real' (\x. x) x0 x0
%   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. happ _0 x = x) ==> (!x0. 'h4/const/lim/tends_real_real' _0 x0 x0)
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_3f59311,V_3f59307]: ![F, G]: (![X]: s(V_3f59307,happ(s(fun(V_3f59311,V_3f59307),F),s(V_3f59311,X))) = s(V_3f59307,happ(s(fun(V_3f59311,V_3f59307),G),s(V_3f59311,X))) => s(fun(V_3f59311,V_3f59307),F) = s(fun(V_3f59311,V_3f59307),G))).
fof('h4/thm/lim/LIM_X_', conjecture, ![V__0]: (![X]: s('h4/type/realax/real',happ(s(fun('h4/type/realax/real','h4/type/realax/real'),V__0),s('h4/type/realax/real',X))) = s('h4/type/realax/real',X) => ![X0]: p(s(bool,'h4/const/lim/tends_real_real'(s(fun('h4/type/realax/real','h4/type/realax/real'),V__0),s('h4/type/realax/real',X0),s('h4/type/realax/real',X0)))))).
