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affeldt-aist merged 2 commits into from
Jun 24, 2025
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lemma generalization #1648

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b4dc185
lemma generalization
affeldt-aist Jun 24, 2025
649b5cf
Update classical/set_interval.v
affeldt-aist Jun 24, 2025
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6 changes: 6 additions & 0 deletions CHANGELOG_UNRELEASED.md
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Expand Up @@ -86,6 +86,9 @@
`le0_nondecreasing_set_nonincreasing_integral`,
`le0_nondecreasing_set_cvg_integral`

- in `set_interval.v`:
+ lemma `memB_itv`, `memB_itv0`

### Changed

- in `convex.v`:
Expand Down Expand Up @@ -236,6 +239,9 @@

### Deprecated

- in `set_interval.v`:
+ lemma `mem_1B_itvcc`

### Removed

- in `measure.v`:
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19 changes: 17 additions & 2 deletions classical/set_interval.v
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Expand Up @@ -535,8 +535,21 @@ Section line_path_factor_numDomainType.
Variable R : numDomainType.
Implicit Types (a b t r : R) (A : set R).

Lemma mem_1B_itvcc t : (1 - t \in `[0, 1]) = (t \in `[0, 1]).
Proof. by rewrite !in_itv/= subr_ge0 gerDl oppr_le0 andbC. Qed.
Lemma memB_itv (x y : bool) a b t :
(b - t \in Interval (BSide x a) (BSide y b)) =
(a + t \in Interval (BSide (~~ y) a) (BSide (~~ x) b)).
Proof.
rewrite !in_itv/= /Order.lteif !if_neg.
by rewrite gerBl gtrBl lerDl ltrDl lerBrDr ltrBrDr andbC.
Qed.

Lemma memB_itv0 (x y : bool) (a b : R) :
(b - a \in Interval (BSide x 0) (BSide y b)) =
(a \in Interval (BSide (~~ y) 0) (BSide (~~ x) b)).
Proof. by rewrite memB_itv add0r. Qed.

Lemma __deprepcated__mem_1B_itvcc t : (1 - t \in `[0, 1]) = (t \in `[0, 1]).
Proof. exact: memB_itv0. Qed.

Definition line_path a b t : R := (1 - t) * a + t * b.

Expand Down Expand Up @@ -591,6 +604,8 @@ Lemma ndline_pathE a b (ab : a < b) : ndline_path ab = line_path a b.
Proof. by []. Qed.

End line_path_factor_numDomainType.
#[deprecated(since="mathcomp-analysis 1.12.0", note="use `memB_itv0` instead")]
Notation mem_1B_itvcc := __deprepcated__mem_1B_itvcc (only parsing).

Section line_path_factor_numFieldType.
Variable R : numFieldType.
Expand Down