generalize indexing in lemmas for series #1397
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Two lemmas for |
affeldt-aist
approved these changes
Dec 6, 2024
CohenCyril
reviewed
Dec 17, 2024
classical/mathcomp_extra.v
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| Lemma eq_lt_total {disp : unit} {T : orderType disp} (x y : T) : | ||
| [|| x == y, (x < y)%O | (y < x)%O]. | ||
| Proof. by case/boolP: (x == y)=> // ?; apply/orP; right; exact:lt_total. Qed. | ||
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| Lemma le_lt_total {disp : unit} {T : orderType disp} (x y : T) : | ||
| (x <= y)%O || (y < x)%O. | ||
| Proof. by rewrite le_eqVlt -orbA eq_lt_total. Qed. |
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The idiomatic ways to deal with this is to use case: ltgtP or case: leP.
CohenCyril
reviewed
Dec 17, 2024
| @@ -951,13 +951,15 @@ rewrite -(subrr (limn (series u_))). | |||
| by apply: cvgB => //; rewrite ?cvg_shiftS. | |||
| Qed. | |||
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| Lemma nondecreasing_series (R : numFieldType) (u_ : R ^nat) (P : pred nat) : | |||
| Lemma nondecreasing_series (R : numFieldType) (u_ : R ^nat) (P : pred nat) m : | |||
| (forall n, P n -> 0 <= u_ n)%R -> | |||
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Why not having
Suggested change
| (forall n, P n -> 0 <= u_ n)%R -> | |
| (forall n, m <= n -> P n -> 0 <= u_ n)%R -> |
instead as a side-condition ?
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Indeed. Several other statements can be similarly generalized. I'll work on that.
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Motivation for this change
There are several lemmas for series stated with zero-based indexing
0 <= k < nandn <oo.This PR generalizes them to
m <= k < nandm <= n<oo.Checklist
CHANGELOG_UNRELEASED.mdReference: How to document
Reminder to reviewers