proposition: Lemma combine_assoc_existT: forall sz1 (w1: word sz1) sz2 (w2: word sz2) sz3 (w3: word sz3), existT word (sz1 + (sz2 + sz3)) (combine w1 (combine w2 w3)) = existT word (sz1 + sz2 + sz3) (combine (combine w1 w2) w3).
proof: Proof. intros; apply EqdepFacts.eq_sigT_sig_eq. assert (Hsz: sz1 + (sz2 + sz3) = sz1 + sz2 + sz3) by lia. exists Hsz. rewrite (combine_assoc w1 w2 w3 Hsz). 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