proposition: Lemma drop_sub_N: forall sz (n k : N), (k * Npow2 sz <= n)%N -> NToWord sz (n - k * Npow2 sz) = NToWord sz n.
proof: Proof. intros. apply wordToN_inj. pose proof (Npow2_not_zero sz). do 2 rewrite wordToN_NToWord_eqn. rewrite <- Nminus_mod_idemp_r by assumption. rewrite N.mod_mul by assumption. rewrite N.sub_0_r. reflexivity. 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