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rm redundant lemma
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affeldt-aist committed Aug 5, 2024
1 parent 73f8d11 commit 13d76d9
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3 changes: 0 additions & 3 deletions CHANGELOG_UNRELEASED.md
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Expand Up @@ -113,9 +113,6 @@
- in `classical_sets.v`:
+ lemmas `xsectionP`, `ysectionP`

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

- in `realfun.v`:
+ lemmas `nondecreasing_at_left_at_right`, `nonincreasing_at_left_at_right`

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7 changes: 0 additions & 7 deletions classical/set_interval.v
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Expand Up @@ -207,13 +207,6 @@ move=> /andP[]; rewrite lt_neqAle => /andP[xz zx ->].
by rewrite andbT; split => //; exact/nesym/eqP.
Qed.

Lemma subset_itv_oo_ccW x y u v : (u <= x)%O -> (y <= v)%O ->
`]x, y[ `<=` `[u, v].
Proof.
move=> ux yv; apply: (subset_trans _ (@subset_itv_oo_cc _ _ _ _)) => z/=.
by rewrite !in_itv/= => /andP[? zy]; rewrite (le_lt_trans ux) ?(lt_le_trans zy).
Qed.

End set_itv_porderType.
Arguments neitv {d T} _.

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12 changes: 6 additions & 6 deletions theories/realfun.v
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Expand Up @@ -386,11 +386,11 @@ Let nondecreasing_at_right_is_cvgrW f a b r : a < r -> r < b ->
Proof.
move=> ar rb ndf H; apply: nondecreasing_at_right_is_cvgr.
- near=> s => x y xrs yrs xy; rewrite ndf//.
+ by apply: subset_itv_oo_ccW xrs; exact/ltW.
+ by apply: subset_itv_oo_ccW yrs; exact/ltW.
+ by apply: subset_itvW xrs; exact/ltW.
+ by apply: subset_itvW yrs; exact/ltW.
- near=> x; exists (f r) => _ /= [s srx <-]; rewrite ndf//.
+ by apply: subset_itv_oo_cc; rewrite in_itv/= ar.
+ by apply: subset_itv_oo_ccW srx; exact/ltW.
+ by apply: subset_itvW srx; exact/ltW.
+ by move: srx; rewrite in_itv/= => /andP[/ltW].
Unshelve. all: by end_near. Qed.

Expand All @@ -399,10 +399,10 @@ Let nondecreasing_at_left_is_cvgrW f a b r : a < r -> r < b ->
Proof.
move=> ar rb ndf H; apply: nondecreasing_at_left_is_cvgr.
- near=> s => x y xrs yrs xy; rewrite ndf//.
+ by apply: subset_itv_oo_ccW xrs; exact/ltW.
+ by apply: subset_itv_oo_ccW yrs; exact/ltW.
+ by apply: subset_itvW xrs; exact/ltW.
+ by apply: subset_itvW yrs; exact/ltW.
- near=> x; exists (f r) => _ /= [s srx <-]; rewrite ndf//.
+ by apply: subset_itv_oo_ccW srx; exact/ltW.
+ by apply: subset_itvW srx; exact/ltW.
+ by apply: subset_itv_oo_cc; rewrite in_itv/= ar.
+ by move: srx; rewrite in_itv/= => /andP[_ /ltW].
Unshelve. all: by end_near. Qed.
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