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(* 02110-1301 USA                                                     *)
(** %\subsection*{ support :  omit\_facts.v }%*)
Set Implicit Arguments.
Unset Strict Implicit.
From Algebra Require Field_facts.
Export Sets Categories Parts Sgroup_cat Monoid_cat Group_cat Abelian_group_cat Ring_cat.
Export Field_facts.
From Algebra Require Ring_facts.
Export Ring_facts.
From Algebra Require Export Field_cat.
Require Export seq_equality_facts.
Require Export sums.
Require Export mult_by_scalars.
destruct n.
simpl in |- *.
red in |- *; auto with algebra.
destruct n.
intros; (apply Trans with (empty_seq M); auto with algebra).
auto with algebra.
Qed.
Hint Resolve omit_head_is_seqtl: algebra.

Lemma omit_tlelt :
forall (n : Nat) (A : Setoid) (v : seq (S (S n)) A)
(m : Nat) (HS : S m < S (S n)) (H : m < S n),
omit v (Build_finiteT HS) =' head v;; omit (Seqtl v) (Build_finiteT H) in _.