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adapt to mc#19611
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Tragicus committed Nov 19, 2024
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Showing 1 changed file with 7 additions and 9 deletions.
16 changes: 7 additions & 9 deletions theories/tvs.v
Original file line number Diff line number Diff line change
Expand Up @@ -124,18 +124,16 @@ Definition entourage : set_system (E * E) :=
(forall xy : E * E, (xy.1 - xy.2) \in U -> xy \in P).

Let nbhs0N (U : set E) : nbhs (0 : E) U -> nbhs (0 : E) (-%R @` U).
Proof. by apply: nbhs0N_subproof; exact: scale_continuous. Qed.
Proof. by apply: (@nbhs0N_subproof _ _ (GRing.Lmodule.class E)); exact: scale_continuous. Qed.

Lemma nbhsN (U : set E) (x : E) : nbhs x U -> nbhs (-x) (-%R @` U).
Proof.
by apply: nbhsN_subproof; exact: scale_continuous.
Qed.
Proof. by apply: (@nbhsN_subproof _ _ (GRing.Lmodule.class E)); exact: scale_continuous. Qed.

Let nbhsT (U : set E) (x : E) : nbhs (0 : E) U -> nbhs x (+%R x @`U).
Proof. by apply: nbhsT_subproof; exact: add_continuous. Qed.
Proof. by apply: (@nbhsT_subproof _ _ (GRing.Lmodule.class E)); exact: add_continuous. Qed.

Let nbhsB (U : set E) (z x : E) : nbhs z U -> nbhs (x + z) (+%R x @`U).
Proof. by apply: nbhsB_subproof; exact: add_continuous. Qed.
Proof. by apply: (@nbhsB_subproof _ _ (GRing.Lmodule.class E)); exact: add_continuous. Qed.

Lemma entourage_filter : Filter entourage.
Proof.
Expand Down Expand Up @@ -216,13 +214,13 @@ Section Tvs_numDomain.
Context (R : numDomainType) (E : tvsType R) (U : set E).

Lemma nbhs0N : nbhs 0 U -> nbhs 0 (-%R @` U).
Proof. exact/nbhs0N_subproof/scale_continuous. Qed.
Proof. exact/(@nbhs0N_subproof _ _ (GRing.Lmodule.class E))/scale_continuous. Qed.

Lemma nbhsT (x :E) : nbhs 0 U -> nbhs x (+%R x @` U).
Proof. exact/nbhsT_subproof/add_continuous. Qed.
Proof. exact/(@nbhsT_subproof _ _ (GRing.Lmodule.class E))/add_continuous. Qed.

Lemma nbhsB (z x : E) : nbhs z U -> nbhs (x + z) (+%R x @` U).
Proof. exact/nbhsB_subproof/add_continuous. Qed.
Proof. exact/(@nbhsB_subproof _ _ (GRing.Lmodule.class E))/add_continuous. Qed.

End Tvs_numDomain.

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