proposition: Lemma split1_combine_existT: forall sz n (w: word (n + sz)) sl (wl: word (n + sl)) su (wu: word su), existT word _ w = existT word _ (combine wl wu) -> split1 n _ w = split1 n _ wl.
proof: Proof. intros. pose proof (word_combinable _ _ w). destruct H0 as [? [? ?]]; subst. pose proof (word_combinable _ _ wl). destruct H0 as [? [? ?]]; subst. assert (sz = sl + su) by (apply eq_sigT_fst in H; lia); subst. pose proof (word_combinable _ _ x0). destruct H0 as [? [? ?]]; subst. do 2 rewrite split1_combine. rewrite combine_assoc_existT in H. destruct_existT. assert (split1 _ _ (split1 _ _ (combine (combine x x3) x4)) = split1 _ _ (split1 _ _ (combine (combine x1 x2) wu))) by (rewrite H; reflexivity). repeat rewrite split1_combine in H0. assumption. 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