%   ORIGINAL: 'h4/thm/transc/RPOW_SUC_N_'
% 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: !a n. 'h4/const/realax/real_lt' ('h4/const/real/real_of_num' 'h4/const/num/0') a ==> 'h4/const/transc/rpow' a ('h4/const/realax/real_add' ('h4/const/real/real_of_num' n) ('h4/const/real/real_of_num' ('h4/const/arithmetic/NUMERAL' ('h4/const/arithmetic/BIT1' 'h4/const/arithmetic/ZERO')))) = 'h4/const/real/pow' a ('h4/const/num/SUC' 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: !a n. 'h4/const/realax/real_lt' ('h4/const/real/real_of_num' 'h4/const/num/0') a ==> 'h4/const/transc/rpow' a ('h4/const/realax/real_add' ('h4/const/real/real_of_num' n) ('h4/const/real/real_of_num' ('h4/const/arithmetic/NUMERAL' ('h4/const/arithmetic/BIT1' 'h4/const/arithmetic/ZERO')))) = 'h4/const/real/pow' a ('h4/const/num/SUC' n)
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_3f73214,V_3f73210]: ![F, G]: (![X]: s(V_3f73210,happ(s(fun(V_3f73214,V_3f73210),F),s(V_3f73214,X))) = s(V_3f73210,happ(s(fun(V_3f73214,V_3f73210),G),s(V_3f73214,X))) => s(fun(V_3f73214,V_3f73210),F) = s(fun(V_3f73214,V_3f73210),G))).
fof('h4/thm/transc/RPOW_SUC_N_', conjecture, ![A, N]: (p(s(bool,'h4/const/realax/real_lt'(s('h4/type/realax/real','h4/const/real/real_of_num'(s('h4/type/num/num','h4/const/num/0'))),s('h4/type/realax/real',A)))) => s('h4/type/realax/real','h4/const/transc/rpow'(s('h4/type/realax/real',A),s('h4/type/realax/real','h4/const/realax/real_add'(s('h4/type/realax/real','h4/const/real/real_of_num'(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/pow'(s('h4/type/realax/real',A),s('h4/type/num/num','h4/const/num/SUC'(s('h4/type/num/num',N))))))).
