%   ORIGINAL: 'h4/thm/transc/EXP_FDIFF_'
% 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: 'h4/const/powser/diffs' (\n. 'h4/const/realax/inv' ('h4/const/real/real_of_num' ('h4/const/arithmetic/FACT' n))) = (\n. 'h4/const/realax/inv' ('h4/const/real/real_of_num' ('h4/const/arithmetic/FACT' n)))
%   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. (!n. happ _0 n = 'h4/const/realax/inv' ('h4/const/real/real_of_num' ('h4/const/arithmetic/FACT' n))) ==> (!x. 'h4/const/powser/diffs' _0 x = 'h4/const/realax/inv' ('h4/const/real/real_of_num' ('h4/const/arithmetic/FACT' 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_3f68136,V_3f68132]: ![F, G]: (![X]: s(V_3f68132,happ(s(fun(V_3f68136,V_3f68132),F),s(V_3f68136,X))) = s(V_3f68132,happ(s(fun(V_3f68136,V_3f68132),G),s(V_3f68136,X))) => s(fun(V_3f68136,V_3f68132),F) = s(fun(V_3f68136,V_3f68132),G))).
fof('h4/thm/transc/EXP_FDIFF_', conjecture, ![V__0]: (![N]: s('h4/type/realax/real',happ(s(fun('h4/type/num/num','h4/type/realax/real'),V__0),s('h4/type/num/num',N))) = s('h4/type/realax/real','h4/const/realax/inv'(s('h4/type/realax/real','h4/const/real/real_of_num'(s('h4/type/num/num','h4/const/arithmetic/FACT'(s('h4/type/num/num',N))))))) => ![X]: s('h4/type/realax/real','h4/const/powser/diffs'(s(fun('h4/type/num/num','h4/type/realax/real'),V__0),s('h4/type/num/num',X))) = s('h4/type/realax/real','h4/const/realax/inv'(s('h4/type/realax/real','h4/const/real/real_of_num'(s('h4/type/num/num','h4/const/arithmetic/FACT'(s('h4/type/num/num',X))))))))).
