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fixes #979 (my_ball_le from local lemme to Let) #980

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Merged
affeldt-aist merged 1 commit into from
Jul 18, 2023
Merged

fixes #979 (my_ball_le from local lemme to Let) #980

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3 changes: 3 additions & 0 deletions CHANGELOG_UNRELEASED.md
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Expand Up @@ -162,6 +162,9 @@

### Removed

- in `topology.v`:
+ lemma `my_ball_le` (use `ball_le` instead)

### Infrastructure

### Misc
9 changes: 4 additions & 5 deletions theories/topology.v
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Expand Up @@ -4902,13 +4902,12 @@ Export PseudoMetric.Exports.

Section PseudoMetricUniformity.

Lemma my_ball_le (R : numDomainType) (M : Type) (ent : set (set (M * M)))
Let ball_le (R : numDomainType) (M : Type) (ent : set (set (M * M)))
(m : PseudoMetric.mixin_of R ent) :
forall (x : M), {homo PseudoMetric.ball m x : e1 e2 / e1 <= e2 >-> e1 `<=` e2}.
Proof.
move=> x e1 e2 le12 y xe1_y.
move: le12; rewrite le_eqVlt => /orP [/eqP <- //|].
rewrite -subr_gt0 => lt12.
move=> x e1 e2 + y xe1_y.
rewrite le_eqVlt => /predU1P[<- //|]; rewrite -subr_gt0 => lt12.
rewrite -[e2](subrK e1); apply: PseudoMetric.ball_triangle xe1_y.
suff : PseudoMetric.ball m x (PosNum lt12)%:num x by [].
exact: PseudoMetric.ball_center.
Expand All @@ -4922,7 +4921,7 @@ Next Obligation.
move=> R T ent nbhs nbhsE m; rewrite (PseudoMetric.entourageE m).
apply: filter_from_filter; first by exists 1 => /=.
move=> _ _ /posnumP[e1] /posnumP[e2]; exists (Num.min e1 e2)%:num => //=.
by rewrite subsetI; split=> ?; apply: my_ball_le;
by rewrite subsetI; split=> ?; apply: ball_le;
rewrite -leEsub// le_minl lexx ?orbT.
Qed.
Next Obligation.
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