%   ORIGINAL: 'h4/thm/transc/RPOW_ADD_MUL_'
% 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_mul' ('h4/const/transc/rpow' a ('h4/const/realax/real_add' b c)) ('h4/const/transc/rpow' a ('h4/const/realax/real_neg' b)) = 'h4/const/transc/rpow' a 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_mul' ('h4/const/transc/rpow' a ('h4/const/realax/real_add' b c)) ('h4/const/transc/rpow' a ('h4/const/realax/real_neg' b)) = 'h4/const/transc/rpow' a 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_3f73414,V_3f73410]: ![F, G]: (![X]: s(V_3f73410,happ(s(fun(V_3f73414,V_3f73410),F),s(V_3f73414,X))) = s(V_3f73410,happ(s(fun(V_3f73414,V_3f73410),G),s(V_3f73414,X))) => s(fun(V_3f73414,V_3f73410),F) = s(fun(V_3f73414,V_3f73410),G))).
fof('h4/thm/transc/RPOW_ADD_MUL_', conjecture, ![A, B, C]: s('h4/type/realax/real','h4/const/realax/real_mul'(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',B),s('h4/type/realax/real',C))))),s('h4/type/realax/real','h4/const/transc/rpow'(s('h4/type/realax/real',A),s('h4/type/realax/real','h4/const/realax/real_neg'(s('h4/type/realax/real',B))))))) = s('h4/type/realax/real','h4/const/transc/rpow'(s('h4/type/realax/real',A),s('h4/type/realax/real',C)))).
