proposition: Lemma div_2 a b: b <> 0 -> a < b * 2 -> a >= b -> a / b = 1.
proof: Proof. intros. assert (sth: b * 1 <= a) by lia. pose proof (Nat.div_le_lower_bound a b 1 H sth). pose proof (Nat.div_lt_upper_bound a b 2 H H0). lia. Qed.
imports: Coq.Classes.Morphisms Coq.Classes.Morphisms_Prop Coq.Classes.Equivalence Coq.Arith.PeanoNat Coq.ZArith.BinInt  Coq.Arith.Arith Coq.NArith.NArith Coq.Bool.Bool Coq.ZArith.ZArith Coq.Logic.Eqdep_dec Coq.Logic.EqdepFacts Coq.Program.Tactics Coq.Program.Equality Coq.setoid_ring.Ring Coq.setoid_ring.Ring_polynom bbv.Nomega bbv.ZLib bbv.NatLib bbv.NLib bbv.N_Z_nat_conversions bbv.DepEq bbv.DepEqNat bbv.ReservedNotations Coq.micromega.Lia