%   ORIGINAL: 'h4/thm/lim/DIFF_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: !x. 'h4/const/lim/diffl' (\x0. x0) ('h4/const/real/real_of_num' ('h4/const/arithmetic/NUMERAL' ('h4/const/arithmetic/BIT1' 'h4/const/arithmetic/ZERO'))) 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. (!x0. happ _0 x0 = x0) ==> (!x. 'h4/const/lim/diffl' _0 ('h4/const/real/real_of_num' ('h4/const/arithmetic/NUMERAL' ('h4/const/arithmetic/BIT1' 'h4/const/arithmetic/ZERO'))) 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_3f59936,V_3f59932]: ![F, G]: (![X]: s(V_3f59932,happ(s(fun(V_3f59936,V_3f59932),F),s(V_3f59936,X))) = s(V_3f59932,happ(s(fun(V_3f59936,V_3f59932),G),s(V_3f59936,X))) => s(fun(V_3f59936,V_3f59932),F) = s(fun(V_3f59936,V_3f59932),G))).
fof('h4/thm/lim/DIFF_X_', conjecture, ![V__0]: (![X0]: s('h4/type/realax/real',happ(s(fun('h4/type/realax/real','h4/type/realax/real'),V__0),s('h4/type/realax/real',X0))) = s('h4/type/realax/real',X0) => ![X]: p(s(bool,'h4/const/lim/diffl'(s(fun('h4/type/realax/real','h4/type/realax/real'),V__0),s('h4/type/realax/real','h4/const/real/real_of_num'(s('h4/type/num/num','h4/const/arithmetic/NUMERAL'(s('h4/type/num/num','h4/const/arithmetic/BIT1'(s('h4/type/num/num','h4/const/arithmetic/ZERO'))))))),s('h4/type/realax/real',X)))))).
