proposition: Lemma tricho_compare_eq `{Trichotomy A R} : forall a b : A, compare a b = EQ -> a = b.
proof: Proof. unfold compare,tricho_compare. intros a b;destruct (trichotomy R a b) as [E|[E|E]];auto. - intros E1;destruct (LT_EQ E1). - intros E1;destruct (GT_EQ E1). Qed.
imports: HoTT.Classes.interfaces.abstract_algebra