%   ORIGINAL: 'h4/thm/real/mult_ints_2'
% 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: !b a. 'h4/const/realax/real_mul' ('h4/const/real/real_of_num' a) ('h4/const/realax/real_neg' ('h4/const/real/real_of_num' b)) = 'h4/const/realax/real_neg' ('h4/const/real/real_of_num' ('h4/const/arithmetic/*' a b))
%   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: !b a. 'h4/const/realax/real_mul' ('h4/const/real/real_of_num' a) ('h4/const/realax/real_neg' ('h4/const/real/real_of_num' b)) = 'h4/const/realax/real_neg' ('h4/const/real/real_of_num' ('h4/const/arithmetic/*' a b))
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_3f97854,V_3f97850]: ![F, G]: (![X]: s(V_3f97850,happ(s(fun(V_3f97854,V_3f97850),F),s(V_3f97854,X))) = s(V_3f97850,happ(s(fun(V_3f97854,V_3f97850),G),s(V_3f97854,X))) => s(fun(V_3f97854,V_3f97850),F) = s(fun(V_3f97854,V_3f97850),G))).
fof('h4/thm/real/mult_ints_2', conjecture, ![B, A]: s('h4/type/realax/real','h4/const/realax/real_mul'(s('h4/type/realax/real','h4/const/real/real_of_num'(s('h4/type/num/num',A))),s('h4/type/realax/real','h4/const/realax/real_neg'(s('h4/type/realax/real','h4/const/real/real_of_num'(s('h4/type/num/num',B))))))) = s('h4/type/realax/real','h4/const/realax/real_neg'(s('h4/type/realax/real','h4/const/real/real_of_num'(s('h4/type/num/num','h4/const/arithmetic/*'(s('h4/type/num/num',A),s('h4/type/num/num',B)))))))).
