@@ -5207,7 +5207,7 @@ Section prod_measurable_fun.
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Context d d1 d2 (T : measurableType d) (T1 : measurableType d1)
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(T2 : measurableType d2).
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- Lemma prod_measurable_funP (h : T -> T1 * T2) : measurable_fun setT h <->
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+ Lemma measurable_fun_pairP (h : T -> T1 * T2) : measurable_fun setT h <->
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measurable_fun setT (fst \o h) /\ measurable_fun setT (snd \o h).
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Proof .
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apply: (@iff_trans _ (g_sigma_preimageU (fst \o h) (snd \o h) `<=` measurable)).
@@ -5220,42 +5220,38 @@ apply: (@iff_trans _ (g_sigma_preimageU (fst \o h) (snd \o h) `<=` measurable)).
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by rewrite subUset; split=> [|] A [C mC <-]; [exact: mf1|exact: mf2].
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Qed .
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- Lemma measurable_fun_prod (f : T -> T1) (g : T -> T2) :
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+ Lemma measurable_fun_pair (f : T -> T1) (g : T -> T2) :
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measurable_fun setT f -> measurable_fun setT g ->
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measurable_fun setT (fun x => (f x, g x)).
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- Proof . by move=> mf mg; exact/prod_measurable_funP . Qed .
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+ Proof . by move=> mf mg; exact/measurable_fun_pairP . Qed .
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End prod_measurable_fun.
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- #[deprecated(since="mathcomp-analysis 0.6.3", note="renamed `measurable_fun_prod`")]
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- Notation measurable_fun_pair := measurable_fun_prod (only parsing).
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+ #[deprecated(since="mathcomp-analysis 1.10.0", note="renamed `measurable_fun_pair`")]
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+ Notation measurable_fun_prod := measurable_fun_pair (only parsing).
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+ #[deprecated(since="mathcomp-analysis 1.10.0", note="renamed `pair_measurable_funP`")]
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+ Notation prod_measurable_funP := measurable_fun_pairP (only parsing).
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Section prod_measurable_proj.
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Context d1 d2 (T1 : measurableType d1) (T2 : measurableType d2).
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Lemma measurable_fst : measurable_fun [set: T1 * T2] fst.
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Proof .
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- by have /prod_measurable_funP [] := @measurable_id _ (T1 * T2)%type setT.
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+ by have /measurable_fun_pairP [] := @measurable_id _ (T1 * T2)%type setT.
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Qed .
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#[local] Hint Resolve measurable_fst : core.
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Lemma measurable_snd : measurable_fun [set: T1 * T2] snd.
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Proof .
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- by have /prod_measurable_funP [] := @measurable_id _ (T1 * T2)%type setT.
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+ by have /measurable_fun_pairP [] := @measurable_id _ (T1 * T2)%type setT.
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Qed .
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#[local] Hint Resolve measurable_snd : core.
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Lemma measurable_swap : measurable_fun [set: _] (@swap T1 T2).
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- Proof . exact: measurable_fun_prod . Qed .
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+ Proof . exact: measurable_fun_pair . Qed .
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End prod_measurable_proj.
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Arguments measurable_fst {d1 d2 T1 T2}.
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Arguments measurable_snd {d1 d2 T1 T2}.
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- #[deprecated(since="mathcomp-analysis 0.6.3", note="renamed `measurable_fst`")]
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- Notation measurable_fun_fst := measurable_fst (only parsing).
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- #[deprecated(since="mathcomp-analysis 0.6.3", note="renamed `measurable_snd`")]
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- Notation measurable_fun_snd := measurable_snd (only parsing).
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- #[deprecated(since="mathcomp-analysis 0.6.3", note="renamed `measurable_swap`")]
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- Notation measurable_fun_swap := measurable_swap (only parsing).
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#[global] Hint Extern 0 (measurable_fun _ fst) =>
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solve [apply: measurable_fst] : core.
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#[global] Hint Extern 0 (measurable_fun _ snd) =>
@@ -5278,14 +5274,14 @@ Lemma measurable_pair1 (x : T1) : measurable_fun [set: T2] (pair x).
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Proof .
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have m1pairx : measurable_fun [set: T2] (fst \o pair x) by exact/measurable_cst.
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have m2pairx : measurable_fun [set: T2] (snd \o pair x) by exact/measurable_id.
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- exact/(prod_measurable_funP _) .
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+ exact/measurable_fun_pairP .
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Qed .
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Lemma measurable_pair2 (y : T2) : measurable_fun [set: T1] (pair^~ y).
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Proof .
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have m1pairy : measurable_fun [set: T1] (fst \o pair^~y) by exact/measurable_id.
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have m2pairy : measurable_fun [set: T1] (snd \o pair^~y) by exact/measurable_cst.
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- exact/(prod_measurable_funP _) .
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+ exact/measurable_fun_pairP .
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Qed .
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End partial_measurable_fun.
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