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affeldt-aist merged 1 commit into from
Nov 17, 2024
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proof simplification #1393

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20 changes: 2 additions & 18 deletions theories/normedtype.v
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Expand Up @@ -5428,27 +5428,11 @@ Proof. exact: interval_open. Qed.

Lemma near_in_itvoy :
{in `]a, +oo[, forall y, \forall z \near y, z \in `]a, +oo[}.
Proof.
move=> x ax.
near=> z.
suff : z \in `]a, +oo[%classic by rewrite inE.
near: z.
rewrite near_nbhs.
apply: (@open_in_nearW _ _ `]a, +oo[%classic) => //.
by rewrite inE.
Unshelve. end_near. Qed.
Proof. exact: interval_open. Qed.

Lemma near_in_itvNyo :
{in `]-oo, b[, forall y, \forall z \near y, z \in `]-oo, b[}.
Proof.
move=> x xb.
near=> z.
suff : z \in `]-oo, b[%classic by rewrite inE.
near: z.
rewrite near_nbhs.
apply: (@open_in_nearW _ _ `]-oo, b[%classic) => //.
by rewrite inE/=.
Unshelve. end_near. Qed.
Proof. exact: interval_open. Qed.

End near_in_itv.
#[deprecated(since="mathcomp-analysis 1.7.0",
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