proposition: Corollary BoundedIndex_beq_sym {n Bound} : forall (p q : BoundedIndex (n := n) Bound), BoundedIndex_beq p q = BoundedIndex_beq q p.
proof: Proof. intros; case_eq (BoundedIndex_beq p q); case_eq (BoundedIndex_beq q p); intros; eauto. - apply BoundedIndex_beq_neq_dec in H; apply BoundedIndex_beq_dec in H0; congruence. - apply BoundedIndex_beq_neq_dec in H0; apply BoundedIndex_beq_dec in H; congruence. Qed.
imports: Coq.Lists.List Coq.Strings.String Coq.Arith.Arith Coq.Logic.Eqdep_dec Fiat.Common.ilist Fiat.Common.ilist2