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(* 02110-1301 USA                                                     *)
(** %\subsection*{ support :  cast\_seq\_lengths.v }%*)
Set Implicit Arguments.
Unset Strict Implicit.
Require Export finite.
(** - An important and annoying obstacle when dealing with seqs is that v and w belong to the same setoid only if their types are convertible. This means that v:(seq n A) and w:(seq k A) cannot be compared, even if we have a proof that n=k. We cannot even %{\em state}% the equality because the expression v='w is ill-typed! - In this file we provide tools to convert between sequences (and their indices) of the same length, if only we are given a proof of the fact. Note that these casting-functions get in the way of many useful lemmas, unfortunately... *)
Section MAIN.

Lemma lt_comp : forall m n n' : Nat, m < n -> n =' n' in _ -> m < n'.
intros.