From ae530db0377361ced605a21ab4e4780fc151a25a Mon Sep 17 00:00:00 2001
From: Reynald Affeldt <reynald.affeldt@aist.go.jp>
Date: Tue, 10 Dec 2024 18:25:38 +0900
Subject: [PATCH] minor generalization

---
 classical/classical_sets.v |  1 +
 theories/measure.v         | 15 +++++++++++++--
 2 files changed, 14 insertions(+), 2 deletions(-)

diff --git a/classical/classical_sets.v b/classical/classical_sets.v
index e4dc9adeb..e5e7579d2 100644
--- a/classical/classical_sets.v
+++ b/classical/classical_sets.v
@@ -2602,6 +2602,7 @@ Proof.
 by apply: qcanon; elim/eqPchoice; elim/choicePpointed => [[T F]|T];
    [left; exists (Empty.Pack F) | right; exists T].
 Qed.
+
 Lemma Ppointed : quasi_canonical Type pointedType.
 Proof.
 by apply: qcanon; elim/Peq; elim/eqPpointed => [[T F]|T];
diff --git a/theories/measure.v b/theories/measure.v
index 691b79f9b..702cd1d65 100644
--- a/theories/measure.v
+++ b/theories/measure.v
@@ -1390,11 +1390,22 @@ Qed.
 
 End sigma_ring_lambda_system.
 
+Lemma countable_bigcupT_measurable d (T : sigmaRingType d) (U : choiceType)
+    (F : U -> set T) : countable [set: U] ->
+  (forall i, measurable (F i)) -> measurable (\bigcup_i F i).
+Proof.
+elim/choicePpointed: U => U in F *.
+  by move=> _ _; rewrite empty_eq0 bigcup0.
+move=> /countable_bijP[B] /ppcard_eqP[f] Fm.
+rewrite (reindex_bigcup f^-1%FUN setT)//=; first exact: bigcupT_measurable.
+exact: (@subl_surj _ _ B).
+Qed.
+
 Lemma bigcupT_measurable_rat d (T : sigmaRingType d) (F : rat -> set T) :
   (forall i, measurable (F i)) -> measurable (\bigcup_i F i).
 Proof.
-move=> Fm; have /ppcard_eqP[f] := card_rat.
-by rewrite (reindex_bigcup f^-1%FUN setT)//=; exact: bigcupT_measurable.
+apply: countable_bigcupT_measurable.
+by apply/countable_bijP; exists setT; exact: card_rat.
 Qed.
 
 Section measurable_lemmas.