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restrain the scope of measurable args #1116

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Jan 7, 2024
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restrain the scope of measurable args #1116

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16 changes: 8 additions & 8 deletions theories/lebesgue_measure.v
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Expand Up @@ -492,24 +492,24 @@ Qed.

Lemma measurable_itv (i : interval R) : measurable [set` i].
Proof.
have moc (a b : R) : measurable `]a, b]%classic.
have moc (a b : R) : measurable `]a, b].
by apply: sub_sigma_algebra; apply: is_ocitv.
have mopoo (x : R) : measurable `]x, +oo[%classic.
have mopoo (x : R) : measurable `]x, +oo[.
by rewrite itv_bnd_infty_bigcup; exact: bigcup_measurable.
have mnooc (x : R) : measurable `]-oo, x]%classic.
have mnooc (x : R) : measurable `]-oo, x].
by rewrite -setCitvr; exact/measurableC.
have ooE (a b : R) : `]a, b[%classic = `]a, b]%classic `\ b.
have ooE (a b : R) : `]a, b[%classic = `]a, b] `\ b.
case: (boolP (a < b)) => ab; last by rewrite !set_itv_ge ?set0D.
by rewrite -setUitv1// setUDK// => x [->]; rewrite /= in_itv/= ltxx andbF.
have moo (a b : R) : measurable `]a, b[%classic.
have moo (a b : R) : measurable `]a, b[.
by rewrite ooE; exact: measurableD.
have mcc (a b : R) : measurable `[a, b]%classic.
have mcc (a b : R) : measurable `[a, b].
case: (boolP (a <= b)) => ab; last by rewrite set_itv_ge.
by rewrite -setU1itv//; apply/measurableU.
have mco (a b : R) : measurable `[a, b[%classic.
have mco (a b : R) : measurable `[a, b[.
case: (boolP (a < b)) => ab; last by rewrite set_itv_ge.
by rewrite -setU1itv//; apply/measurableU.
have oooE (b : R) : `]-oo, b[%classic = `]-oo, b]%classic `\ b.
have oooE (b : R) : `]-oo, b[%classic = `]-oo, b] `\ b.
by rewrite -setUitv1// setUDK// => x [->]; rewrite /= in_itv/= ltxx.
case: i => [[[] a|[]] [[] b|[]]] => //; do ?by rewrite set_itv_ge.
- by rewrite -setU1itv//; exact/measurableU.
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2 changes: 2 additions & 0 deletions theories/measure.v
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Expand Up @@ -721,6 +721,8 @@ HB.mixin Record isSemiRingOfSets (d : measure_display) T := {
#[short(type=semiRingOfSetsType)]
HB.structure Definition SemiRingOfSets d := {T of isSemiRingOfSets d T}.

Arguments measurable {d}%measure_display_scope {s} _%classical_set_scope.

Canonical semiRingOfSets_eqType d (T : semiRingOfSetsType d) := EqType T ptclass.
Canonical semiRingOfSets_choiceType d (T : semiRingOfSetsType d) :=
ChoiceType T ptclass.
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