%   ORIGINAL: 'h4/thm/transc/RPOW_DIV_'
% 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 b c. 'h4/const/realax/real_lt' ('h4/const/real/real_of_num' 'h4/const/num/0') a /\ 'h4/const/realax/real_lt' ('h4/const/real/real_of_num' 'h4/const/num/0') b ==> 'h4/const/transc/rpow' ('h4/const/real/#slash#' a b) c = 'h4/const/real/#slash#' ('h4/const/transc/rpow' a c) ('h4/const/transc/rpow' b c)
%   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 b c. 'h4/const/realax/real_lt' ('h4/const/real/real_of_num' 'h4/const/num/0') a /\ 'h4/const/realax/real_lt' ('h4/const/real/real_of_num' 'h4/const/num/0') b ==> 'h4/const/transc/rpow' ('h4/const/real/#slash#' a b) c = 'h4/const/real/#slash#' ('h4/const/transc/rpow' a c) ('h4/const/transc/rpow' b c)
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_3f73464,V_3f73460]: ![F, G]: (![X]: s(V_3f73460,happ(s(fun(V_3f73464,V_3f73460),F),s(V_3f73464,X))) = s(V_3f73460,happ(s(fun(V_3f73464,V_3f73460),G),s(V_3f73464,X))) => s(fun(V_3f73464,V_3f73460),F) = s(fun(V_3f73464,V_3f73460),G))).
fof('h4/thm/transc/RPOW_DIV_', conjecture, ![A, B, C]: ((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)))) & 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',B))))) => s('h4/type/realax/real','h4/const/transc/rpow'(s('h4/type/realax/real','h4/const/real/#slash#'(s('h4/type/realax/real',A),s('h4/type/realax/real',B))),s('h4/type/realax/real',C))) = s('h4/type/realax/real','h4/const/real/#slash#'(s('h4/type/realax/real','h4/const/transc/rpow'(s('h4/type/realax/real',A),s('h4/type/realax/real',C))),s('h4/type/realax/real','h4/const/transc/rpow'(s('h4/type/realax/real',B),s('h4/type/realax/real',C))))))).
