%   ORIGINAL: 'h4/thm/seq/GP_FINITE_'
% 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. ~(x = 'h4/const/real/real_of_num' ('h4/const/arithmetic/NUMERAL' ('h4/const/arithmetic/BIT1' 'h4/const/arithmetic/ZERO'))) ==> (!n. 'h4/const/real/sum' ('h4/const/pair/,' 'h4/const/num/0' n) (\n0. 'h4/const/real/pow' x n0) = 'h4/const/real/#slash#' ('h4/const/real/real_sub' ('h4/const/real/pow' x n) ('h4/const/real/real_of_num' ('h4/const/arithmetic/NUMERAL' ('h4/const/arithmetic/BIT1' 'h4/const/arithmetic/ZERO')))) ('h4/const/real/real_sub' x ('h4/const/real/real_of_num' ('h4/const/arithmetic/NUMERAL' ('h4/const/arithmetic/BIT1' 'h4/const/arithmetic/ZERO')))))
%   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 n0. happ (happ _0 x) n0 = 'h4/const/real/pow' x n0) ==> (!x. ~(x = 'h4/const/real/real_of_num' ('h4/const/arithmetic/NUMERAL' ('h4/const/arithmetic/BIT1' 'h4/const/arithmetic/ZERO'))) ==> (!n. 'h4/const/real/sum' ('h4/const/pair/,' 'h4/const/num/0' n) (happ _0 x) = 'h4/const/real/#slash#' ('h4/const/real/real_sub' ('h4/const/real/pow' x n) ('h4/const/real/real_of_num' ('h4/const/arithmetic/NUMERAL' ('h4/const/arithmetic/BIT1' 'h4/const/arithmetic/ZERO')))) ('h4/const/real/real_sub' x ('h4/const/real/real_of_num' ('h4/const/arithmetic/NUMERAL' ('h4/const/arithmetic/BIT1' 'h4/const/arithmetic/ZERO'))))))
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_3f65786,V_3f65782]: ![F, G]: (![X]: s(V_3f65782,happ(s(fun(V_3f65786,V_3f65782),F),s(V_3f65786,X))) = s(V_3f65782,happ(s(fun(V_3f65786,V_3f65782),G),s(V_3f65786,X))) => s(fun(V_3f65786,V_3f65782),F) = s(fun(V_3f65786,V_3f65782),G))).
fof('h4/thm/seq/GP_FINITE_', conjecture, ![V__0]: (![X, N0]: s('h4/type/realax/real',happ(s(fun('h4/type/num/num','h4/type/realax/real'),happ(s(fun('h4/type/realax/real',fun('h4/type/num/num','h4/type/realax/real')),V__0),s('h4/type/realax/real',X))),s('h4/type/num/num',N0))) = s('h4/type/realax/real','h4/const/real/pow'(s('h4/type/realax/real',X),s('h4/type/num/num',N0))) => ![X]: (~ (s('h4/type/realax/real',X) = 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')))))))) => ![N]: s('h4/type/realax/real','h4/const/real/sum'(s('h4/type/pair/prod'('h4/type/num/num','h4/type/num/num'),'h4/const/pair/,'(s('h4/type/num/num','h4/const/num/0'),s('h4/type/num/num',N))),s(fun('h4/type/num/num','h4/type/realax/real'),happ(s(fun('h4/type/realax/real',fun('h4/type/num/num','h4/type/realax/real')),V__0),s('h4/type/realax/real',X))))) = s('h4/type/realax/real','h4/const/real/#slash#'(s('h4/type/realax/real','h4/const/real/real_sub'(s('h4/type/realax/real','h4/const/real/pow'(s('h4/type/realax/real',X),s('h4/type/num/num',N))),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','h4/const/real/real_sub'(s('h4/type/realax/real',X),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')))))))))))))).
