proposition: Lemma split2_le sz1 sz2: forall (w1 w2: word (sz1 + sz2)), (w1 <= w2 -> split2 _ _ w1 <= split2 _ _ w2)%word.
proof: Proof. intros. pre_word_omega. rewrite ?wordToNat_split2. pose proof (pow2_zero sz1). apply Nat.div_le_mono; auto. Lia.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