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remove MathComp duplicate #368

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affeldt-aist opened this issue Apr 26, 2021 · 1 comment
Closed

remove MathComp duplicate #368

affeldt-aist opened this issue Apr 26, 2021 · 1 comment

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@affeldt-aist
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remove [1] when math-comp/math-comp#737 is merged into MathComp

--
[1]

(* TODO: add to bigop.v *)
Lemma big_nat_widenl (R : Type) (idx : R) (op : Monoid.law idx) (m1 m2 n : nat)
(P : pred nat) (F : nat -> R) :
m2 <= m1 ->
\big[op/idx]_(m1 <= i < n | P i) F i =
\big[op/idx]_(m2 <= i < n | P i && (m1 <= i)) F i.
Proof.
move=> le_m21; have [le_nm1|lt_m1n] := leqP n m1.
rewrite big_geq// big_nat_cond big1//.
by move=> i /and3P[/andP[_ /leq_trans/(_ le_nm1)/ltn_geF->]].
rewrite big_mkcond big_mkcondl (big_cat_nat _ _ _ le_m21) 1?ltnW//.
rewrite [X in op X]big_nat_cond [X in op X]big_pred0; last first.
by move=> k; case: ltnP; rewrite andbF.
by rewrite Monoid.mul1m; apply: congr_big_nat => // k /andP[].
Qed.
Arguments big_nat_widenl [R idx op].
(* TODO: add to bigop.v *)
Lemma big_geq_mkord (R : Type) (idx : R) (op : Monoid.law idx) (m n : nat)
(P : pred nat) (F : nat -> R) :
\big[op/idx]_(m <= i < n | P i) F i =
\big[op/idx]_(i < n | P i && (m <= i)) F i.
Proof. by rewrite (big_nat_widenl _ 0)// big_mkord. Qed.

@CohenCyril
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fixed by #542

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2 participants