proposition: Lemma mul_sub_distr_l p q r : r<q -> p*(q-r) = p*q-p*r.
proof: Proof. intros H. apply add_reg_r with (p*r). rewrite <- mul_add_distr_l. rewrite sub_add; trivial. symmetry. apply sub_add; trivial. now apply mul_lt_mono_l. Qed.
imports: BinNums Eqdep_dec EqdepFacts RelationClasses Morphisms Setoid Equalities Orders OrdersFacts GenericMinMax PeanoNat BinPosDef