%   ORIGINAL: 'h4/thm/lim/LIM_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: !k x. 'h4/const/lim/tends_real_real' (\x0. k) k 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. (!k x0. happ (happ _0 k) x0 = k) ==> (!k x. 'h4/const/lim/tends_real_real' (happ _0 k) k 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_3f59111,V_3f59107]: ![F, G]: (![X]: s(V_3f59107,happ(s(fun(V_3f59111,V_3f59107),F),s(V_3f59111,X))) = s(V_3f59107,happ(s(fun(V_3f59111,V_3f59107),G),s(V_3f59111,X))) => s(fun(V_3f59111,V_3f59107),F) = s(fun(V_3f59111,V_3f59107),G))).
fof('h4/thm/lim/LIM_CONST_', conjecture, ![V__0]: (![K, X0]: s('h4/type/realax/real',happ(s(fun('h4/type/realax/real','h4/type/realax/real'),happ(s(fun('h4/type/realax/real',fun('h4/type/realax/real','h4/type/realax/real')),V__0),s('h4/type/realax/real',K))),s('h4/type/realax/real',X0))) = s('h4/type/realax/real',K) => ![K, X]: p(s(bool,'h4/const/lim/tends_real_real'(s(fun('h4/type/realax/real','h4/type/realax/real'),happ(s(fun('h4/type/realax/real',fun('h4/type/realax/real','h4/type/realax/real')),V__0),s('h4/type/realax/real',K))),s('h4/type/realax/real',K),s('h4/type/realax/real',X)))))).
