proposition: Lemma mod2_cases: forall (n: nat), n mod 2 = 0 \/ n mod 2 = 1.
proof: Proof. intros. assert (n mod 2 < 2). { apply Nat.mod_upper_bound. congruence. } lia. Qed.
imports: Coq.Classes.Morphisms Coq.Classes.Morphisms_Prop Coq.Bool.Bool Coq.Arith.Arith Coq.micromega.Lia Coq.NArith.NArith Coq.ZArith.ZArith bbv.N_Z_nat_conversions bbv.Nomega