probability.probability_mass_function.monad ⟷ Mathlib.Probability.ProbabilityMassFunction.Monad

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -363,7 +363,7 @@ theorem bindOnSupport_bindOnSupport (p : PMF α) (f : ∀ a ∈ p.support, PMF 
   refine' ennreal.tsum_comm.trans (tsum_congr fun a' => tsum_congr fun b => _)
   split_ifs
   any_goals ring1
-  · have := h_1 a'; simp [h] at this ; contradiction
+  · have := h_1 a'; simp [h] at this; contradiction
   · simp [h_2]
 #align pmf.bind_on_support_bind_on_support PMF.bindOnSupport_bindOnSupport
 -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -358,7 +358,7 @@ theorem bindOnSupport_bindOnSupport (p : PMF α) (f : ∀ a ∈ p.support, PMF 
   refine' PMF.ext fun a => _
   simp only [ennreal.coe_eq_coe.symm, bind_on_support_apply, ← tsum_dite_right,
     ennreal.tsum_mul_left.symm, ennreal.tsum_mul_right.symm]
-  simp only [ENNReal.tsum_eq_zero, ENNReal.coe_eq_coe, ENNReal.coe_eq_zero, ENNReal.coe_zero,
+  simp only [ENNReal.tsum_eq_zero, ENNReal.coe_inj, ENNReal.coe_eq_zero, ENNReal.coe_zero,
     dite_eq_left_iff, mul_eq_zero]
   refine' ennreal.tsum_comm.trans (tsum_congr fun a' => tsum_congr fun b => _)
   split_ifs

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -322,7 +322,8 @@ theorem bindOnSupport_eq_bind (p : PMF α) (f : α → PMF β) :
 theorem bindOnSupport_eq_zero_iff (b : β) :
     p.bindOnSupport f b = 0 ↔ ∀ (a) (ha : p a ≠ 0), f a ha b = 0 :=
   by
-  simp only [bind_on_support_apply, ENNReal.tsum_eq_zero, mul_eq_zero, or_iff_not_imp_left]
+  simp only [bind_on_support_apply, ENNReal.tsum_eq_zero, mul_eq_zero,
+    Classical.or_iff_not_imp_left]
   exact ⟨fun h a ha => trans (dif_neg ha).symm (h a ha), fun h a ha => trans (dif_neg ha) (h a ha)⟩
 #align pmf.bind_on_support_eq_zero_iff PMF.bindOnSupport_eq_zero_iff
 -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/b1abe23ae96fef89ad30d9f4362c307f72a55010

@@ -286,7 +286,7 @@ theorem support_bindOnSupport :
   by
   refine' Set.ext fun b => _
   simp only [ENNReal.tsum_eq_zero, not_or, mem_support_iff, bind_on_support_apply, Ne.def,
-    not_forall, mul_eq_zero, Set.mem_iUnion]
+    Classical.not_forall, mul_eq_zero, Set.mem_iUnion]
   exact
     ⟨fun hb =>
       let ⟨a, ⟨ha, ha'⟩⟩ := hb

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451

@@ -32,60 +32,60 @@ open scoped Classical BigOperators NNReal ENNReal
 
 open MeasureTheory
 
-namespace Pmf
+namespace PMF
 
 section Pure
 
-#print Pmf.pure /-
+#print PMF.pure /-
 /-- The pure `pmf` is the `pmf` where all the mass lies in one point.
   The value of `pure a` is `1` at `a` and `0` elsewhere. -/
-def pure (a : α) : Pmf α :=
+def pure (a : α) : PMF α :=
   ⟨fun a' => if a' = a then 1 else 0, hasSum_ite_eq _ _⟩
-#align pmf.pure Pmf.pure
+#align pmf.pure PMF.pure
 -/
 
 variable (a a' : α)
 
-#print Pmf.pure_apply /-
+#print PMF.pure_apply /-
 @[simp]
 theorem pure_apply : pure a a' = if a' = a then 1 else 0 :=
   rfl
-#align pmf.pure_apply Pmf.pure_apply
+#align pmf.pure_apply PMF.pure_apply
 -/
 
-#print Pmf.support_pure /-
+#print PMF.support_pure /-
 @[simp]
 theorem support_pure : (pure a).support = {a} :=
   Set.ext fun a' => by simp [mem_support_iff]
-#align pmf.support_pure Pmf.support_pure
+#align pmf.support_pure PMF.support_pure
 -/
 
-#print Pmf.mem_support_pure_iff /-
+#print PMF.mem_support_pure_iff /-
 theorem mem_support_pure_iff : a' ∈ (pure a).support ↔ a' = a := by simp
-#align pmf.mem_support_pure_iff Pmf.mem_support_pure_iff
+#align pmf.mem_support_pure_iff PMF.mem_support_pure_iff
 -/
 
-#print Pmf.pure_apply_self /-
+#print PMF.pure_apply_self /-
 @[simp]
 theorem pure_apply_self : pure a a = 1 :=
   if_pos rfl
-#align pmf.pure_apply_self Pmf.pure_apply_self
+#align pmf.pure_apply_self PMF.pure_apply_self
 -/
 
-#print Pmf.pure_apply_of_ne /-
+#print PMF.pure_apply_of_ne /-
 theorem pure_apply_of_ne (h : a' ≠ a) : pure a a' = 0 :=
   if_neg h
-#align pmf.pure_apply_of_ne Pmf.pure_apply_of_ne
+#align pmf.pure_apply_of_ne PMF.pure_apply_of_ne
 -/
 
-instance [Inhabited α] : Inhabited (Pmf α) :=
+instance [Inhabited α] : Inhabited (PMF α) :=
   ⟨pure default⟩
 
 section Measure
 
 variable (s : Set α)
 
-#print Pmf.toOuterMeasure_pure_apply /-
+#print PMF.toOuterMeasure_pure_apply /-
 @[simp]
 theorem toOuterMeasure_pure_apply : (pure a).toOuterMeasure s = if a ∈ s then 1 else 0 :=
   by
@@ -95,31 +95,31 @@ theorem toOuterMeasure_pure_apply : (pure a).toOuterMeasure s = if a ∈ s then
     exact ite_eq_left_iff.2 fun hb => symm (ite_eq_right_iff.2 fun h => (hb <| h.symm ▸ ha).elim)
   · refine' (tsum_congr fun b => _).trans tsum_zero
     exact ite_eq_right_iff.2 fun hb => ite_eq_right_iff.2 fun h => (ha <| h ▸ hb).elim
-#align pmf.to_outer_measure_pure_apply Pmf.toOuterMeasure_pure_apply
+#align pmf.to_outer_measure_pure_apply PMF.toOuterMeasure_pure_apply
 -/
 
 variable [MeasurableSpace α]
 
-#print Pmf.toMeasure_pure_apply /-
+#print PMF.toMeasure_pure_apply /-
 /-- The measure of a set under `pure a` is `1` for sets containing `a` and `0` otherwise -/
 @[simp]
 theorem toMeasure_pure_apply (hs : MeasurableSet s) :
     (pure a).toMeasure s = if a ∈ s then 1 else 0 :=
   (toMeasure_apply_eq_toOuterMeasure_apply (pure a) s hs).trans (toOuterMeasure_pure_apply a s)
-#align pmf.to_measure_pure_apply Pmf.toMeasure_pure_apply
+#align pmf.to_measure_pure_apply PMF.toMeasure_pure_apply
 -/
 
-#print Pmf.toMeasure_pure /-
+#print PMF.toMeasure_pure /-
 theorem toMeasure_pure : (pure a).toMeasure = Measure.dirac a :=
   Measure.ext fun s hs => by simpa only [to_measure_pure_apply a s hs, measure.dirac_apply' a hs]
-#align pmf.to_measure_pure Pmf.toMeasure_pure
+#align pmf.to_measure_pure PMF.toMeasure_pure
 -/
 
-#print Pmf.toPmf_dirac /-
+#print PMF.toPMF_dirac /-
 @[simp]
-theorem toPmf_dirac [Countable α] [h : MeasurableSingletonClass α] :
-    (Measure.dirac a).toPmf = pure a := by rw [to_pmf_eq_iff_to_measure_eq, to_measure_pure]
-#align pmf.to_pmf_dirac Pmf.toPmf_dirac
+theorem toPMF_dirac [Countable α] [h : MeasurableSingletonClass α] :
+    (Measure.dirac a).toPMF = pure a := by rw [to_pmf_eq_iff_to_measure_eq, to_measure_pure]
+#align pmf.to_pmf_dirac PMF.toPMF_dirac
 -/
 
 end Measure
@@ -128,83 +128,83 @@ end Pure
 
 section Bind
 
-#print Pmf.bind /-
+#print PMF.bind /-
 /-- The monadic bind operation for `pmf`. -/
-def bind (p : Pmf α) (f : α → Pmf β) : Pmf β :=
+def bind (p : PMF α) (f : α → PMF β) : PMF β :=
   ⟨fun b => ∑' a, p a * f a b,
     ENNReal.summable.hasSum_iff.2
       (ENNReal.tsum_comm.trans <| by simp only [ENNReal.tsum_mul_left, tsum_coe, mul_one])⟩
-#align pmf.bind Pmf.bind
+#align pmf.bind PMF.bind
 -/
 
-variable (p : Pmf α) (f : α → Pmf β) (g : β → Pmf γ)
+variable (p : PMF α) (f : α → PMF β) (g : β → PMF γ)
 
-#print Pmf.bind_apply /-
+#print PMF.bind_apply /-
 @[simp]
 theorem bind_apply (b : β) : p.bind f b = ∑' a, p a * f a b :=
   rfl
-#align pmf.bind_apply Pmf.bind_apply
+#align pmf.bind_apply PMF.bind_apply
 -/
 
-#print Pmf.support_bind /-
+#print PMF.support_bind /-
 @[simp]
 theorem support_bind : (p.bind f).support = ⋃ a ∈ p.support, (f a).support :=
   Set.ext fun b => by simp [mem_support_iff, ENNReal.tsum_eq_zero, not_or]
-#align pmf.support_bind Pmf.support_bind
+#align pmf.support_bind PMF.support_bind
 -/
 
-#print Pmf.mem_support_bind_iff /-
+#print PMF.mem_support_bind_iff /-
 theorem mem_support_bind_iff (b : β) :
     b ∈ (p.bind f).support ↔ ∃ a ∈ p.support, b ∈ (f a).support := by
   simp only [support_bind, Set.mem_iUnion, Set.mem_setOf_eq]
-#align pmf.mem_support_bind_iff Pmf.mem_support_bind_iff
+#align pmf.mem_support_bind_iff PMF.mem_support_bind_iff
 -/
 
-#print Pmf.pure_bind /-
+#print PMF.pure_bind /-
 @[simp]
-theorem pure_bind (a : α) (f : α → Pmf β) : (pure a).bind f = f a :=
+theorem pure_bind (a : α) (f : α → PMF β) : (pure a).bind f = f a :=
   by
   have : ∀ b a', ite (a' = a) 1 0 * f a' b = ite (a' = a) (f a b) 0 := fun b a' => by
     split_ifs <;> simp <;> subst h <;> simp
   ext b <;> simp [this]
-#align pmf.pure_bind Pmf.pure_bind
+#align pmf.pure_bind PMF.pure_bind
 -/
 
-#print Pmf.bind_pure /-
+#print PMF.bind_pure /-
 @[simp]
 theorem bind_pure : p.bind pure = p :=
-  Pmf.ext fun x =>
+  PMF.ext fun x =>
     (bind_apply _ _ _).trans
       (trans
           (tsum_eq_single x fun y hy => by
             rw [pure_apply_of_ne _ _ hy.symm, MulZeroClass.mul_zero]) <|
         by rw [pure_apply_self, mul_one])
-#align pmf.bind_pure Pmf.bind_pure
+#align pmf.bind_pure PMF.bind_pure
 -/
 
-#print Pmf.bind_const /-
+#print PMF.bind_const /-
 @[simp]
-theorem bind_const (p : Pmf α) (q : Pmf β) : (p.bind fun _ => q) = q :=
-  Pmf.ext fun x => by rw [bind_apply, ENNReal.tsum_mul_right, tsum_coe, one_mul]
-#align pmf.bind_const Pmf.bind_const
+theorem bind_const (p : PMF α) (q : PMF β) : (p.bind fun _ => q) = q :=
+  PMF.ext fun x => by rw [bind_apply, ENNReal.tsum_mul_right, tsum_coe, one_mul]
+#align pmf.bind_const PMF.bind_const
 -/
 
-#print Pmf.bind_bind /-
+#print PMF.bind_bind /-
 @[simp]
 theorem bind_bind : (p.bind f).bind g = p.bind fun a => (f a).bind g :=
-  Pmf.ext fun b => by
+  PMF.ext fun b => by
     simpa only [ennreal.coe_eq_coe.symm, bind_apply, ennreal.tsum_mul_left.symm,
       ennreal.tsum_mul_right.symm, mul_assoc, mul_left_comm, mul_comm] using ENNReal.tsum_comm
-#align pmf.bind_bind Pmf.bind_bind
+#align pmf.bind_bind PMF.bind_bind
 -/
 
-#print Pmf.bind_comm /-
-theorem bind_comm (p : Pmf α) (q : Pmf β) (f : α → β → Pmf γ) :
+#print PMF.bind_comm /-
+theorem bind_comm (p : PMF α) (q : PMF β) (f : α → β → PMF γ) :
     (p.bind fun a => q.bind (f a)) = q.bind fun b => p.bind fun a => f a b :=
-  Pmf.ext fun b => by
+  PMF.ext fun b => by
     simpa only [ennreal.coe_eq_coe.symm, bind_apply, ennreal.tsum_mul_left.symm,
       ennreal.tsum_mul_right.symm, mul_assoc, mul_left_comm, mul_comm] using ENNReal.tsum_comm
-#align pmf.bind_comm Pmf.bind_comm
+#align pmf.bind_comm PMF.bind_comm
 -/
 
 section Measure
@@ -213,7 +213,7 @@ variable (s : Set β)
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (b a) -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (a b) -/
-#print Pmf.toOuterMeasure_bind_apply /-
+#print PMF.toOuterMeasure_bind_apply /-
 @[simp]
 theorem toOuterMeasure_bind_apply :
     (p.bind f).toOuterMeasure s = ∑' a, p a * (f a).toOuterMeasure s :=
@@ -228,10 +228,10 @@ theorem toOuterMeasure_bind_apply :
       (tsum_congr fun a => (congr_arg fun x => p a * x) <| tsum_congr fun b => by split_ifs <;> rfl)
     _ = ∑' a, p a * (f a).toOuterMeasure s :=
       tsum_congr fun a => by simp only [to_outer_measure_apply, Set.indicator_apply]
-#align pmf.to_outer_measure_bind_apply Pmf.toOuterMeasure_bind_apply
+#align pmf.to_outer_measure_bind_apply PMF.toOuterMeasure_bind_apply
 -/
 
-#print Pmf.toMeasure_bind_apply /-
+#print PMF.toMeasure_bind_apply /-
 /-- The measure of a set under `p.bind f` is the sum over `a : α`
   of the probability of `a` under `p` times the measure of the set under `f a` -/
 @[simp]
@@ -241,23 +241,23 @@ theorem toMeasure_bind_apply [MeasurableSpace β] (hs : MeasurableSet s) :
     ((toOuterMeasure_bind_apply p f s).trans
       (tsum_congr fun a =>
         congr_arg (fun x => p a * x) (toMeasure_apply_eq_toOuterMeasure_apply (f a) s hs).symm))
-#align pmf.to_measure_bind_apply Pmf.toMeasure_bind_apply
+#align pmf.to_measure_bind_apply PMF.toMeasure_bind_apply
 -/
 
 end Measure
 
 end Bind
 
-instance : Monad Pmf where
+instance : Monad PMF where
   pure A a := pure a
   bind A B pa pb := pa.bind pb
 
 section BindOnSupport
 
-#print Pmf.bindOnSupport /-
+#print PMF.bindOnSupport /-
 /-- Generalized version of `bind` allowing `f` to only be defined on the support of `p`.
   `p.bind f` is equivalent to `p.bind_on_support (λ a _, f a)`, see `bind_on_support_eq_bind` -/
-def bindOnSupport (p : Pmf α) (f : ∀ a ∈ p.support, Pmf β) : Pmf β :=
+def bindOnSupport (p : PMF α) (f : ∀ a ∈ p.support, PMF β) : PMF β :=
   ⟨fun b => ∑' a, p a * if h : p a = 0 then 0 else f a h b,
     ENNReal.summable.hasSum_iff.2
       (by
@@ -266,20 +266,20 @@ def bindOnSupport (p : Pmf α) (f : ∀ a ∈ p.support, Pmf β) : Pmf β :=
         split_ifs with h
         · simp only [h, MulZeroClass.zero_mul]
         · rw [(f a h).tsum_coe, mul_one])⟩
-#align pmf.bind_on_support Pmf.bindOnSupport
+#align pmf.bind_on_support PMF.bindOnSupport
 -/
 
-variable {p : Pmf α} (f : ∀ a ∈ p.support, Pmf β)
+variable {p : PMF α} (f : ∀ a ∈ p.support, PMF β)
 
-#print Pmf.bindOnSupport_apply /-
+#print PMF.bindOnSupport_apply /-
 @[simp]
 theorem bindOnSupport_apply (b : β) :
     p.bindOnSupport f b = ∑' a, p a * if h : p a = 0 then 0 else f a h b :=
   rfl
-#align pmf.bind_on_support_apply Pmf.bindOnSupport_apply
+#align pmf.bind_on_support_apply PMF.bindOnSupport_apply
 -/
 
-#print Pmf.support_bindOnSupport /-
+#print PMF.support_bindOnSupport /-
 @[simp]
 theorem support_bindOnSupport :
     (p.bindOnSupport f).support = ⋃ (a : α) (h : a ∈ p.support), (f a h).support :=
@@ -294,20 +294,20 @@ theorem support_bindOnSupport :
       fun hb =>
       let ⟨a, ha, ha'⟩ := hb
       ⟨a, ⟨ha, by simpa [(mem_support_iff _ a).1 ha] using ha'⟩⟩⟩
-#align pmf.support_bind_on_support Pmf.support_bindOnSupport
+#align pmf.support_bind_on_support PMF.support_bindOnSupport
 -/
 
-#print Pmf.mem_support_bindOnSupport_iff /-
+#print PMF.mem_support_bindOnSupport_iff /-
 theorem mem_support_bindOnSupport_iff (b : β) :
     b ∈ (p.bindOnSupport f).support ↔ ∃ (a : α) (h : a ∈ p.support), b ∈ (f a h).support := by
   simp only [support_bind_on_support, Set.mem_setOf_eq, Set.mem_iUnion]
-#align pmf.mem_support_bind_on_support_iff Pmf.mem_support_bindOnSupport_iff
+#align pmf.mem_support_bind_on_support_iff PMF.mem_support_bindOnSupport_iff
 -/
 
-#print Pmf.bindOnSupport_eq_bind /-
+#print PMF.bindOnSupport_eq_bind /-
 /-- `bind_on_support` reduces to `bind` if `f` doesn't depend on the additional hypothesis -/
 @[simp]
-theorem bindOnSupport_eq_bind (p : Pmf α) (f : α → Pmf β) :
+theorem bindOnSupport_eq_bind (p : PMF α) (f : α → PMF β) :
     (p.bindOnSupport fun a _ => f a) = p.bind f :=
   by
   ext b x
@@ -315,46 +315,46 @@ theorem bindOnSupport_eq_bind (p : Pmf α) (f : α → Pmf β) :
     ite_eq_right_iff.2 fun h => h.symm ▸ symm (MulZeroClass.zero_mul <| f a b)
   simp only [bind_on_support_apply fun a _ => f a, p.bind_apply f, dite_eq_ite, mul_ite,
     MulZeroClass.mul_zero, this]
-#align pmf.bind_on_support_eq_bind Pmf.bindOnSupport_eq_bind
+#align pmf.bind_on_support_eq_bind PMF.bindOnSupport_eq_bind
 -/
 
-#print Pmf.bindOnSupport_eq_zero_iff /-
+#print PMF.bindOnSupport_eq_zero_iff /-
 theorem bindOnSupport_eq_zero_iff (b : β) :
     p.bindOnSupport f b = 0 ↔ ∀ (a) (ha : p a ≠ 0), f a ha b = 0 :=
   by
   simp only [bind_on_support_apply, ENNReal.tsum_eq_zero, mul_eq_zero, or_iff_not_imp_left]
   exact ⟨fun h a ha => trans (dif_neg ha).symm (h a ha), fun h a ha => trans (dif_neg ha) (h a ha)⟩
-#align pmf.bind_on_support_eq_zero_iff Pmf.bindOnSupport_eq_zero_iff
+#align pmf.bind_on_support_eq_zero_iff PMF.bindOnSupport_eq_zero_iff
 -/
 
-#print Pmf.pure_bindOnSupport /-
+#print PMF.pure_bindOnSupport /-
 @[simp]
-theorem pure_bindOnSupport (a : α) (f : ∀ (a' : α) (ha : a' ∈ (pure a).support), Pmf β) :
+theorem pure_bindOnSupport (a : α) (f : ∀ (a' : α) (ha : a' ∈ (pure a).support), PMF β) :
     (pure a).bindOnSupport f = f a ((mem_support_pure_iff a a).mpr rfl) :=
   by
-  refine' Pmf.ext fun b => _
+  refine' PMF.ext fun b => _
   simp only [bind_on_support_apply, pure_apply]
   refine' trans (tsum_congr fun a' => _) (tsum_ite_eq a _)
   by_cases h : a' = a <;> simp [h]
-#align pmf.pure_bind_on_support Pmf.pure_bindOnSupport
+#align pmf.pure_bind_on_support PMF.pure_bindOnSupport
 -/
 
-#print Pmf.bindOnSupport_pure /-
-theorem bindOnSupport_pure (p : Pmf α) : (p.bindOnSupport fun a _ => pure a) = p := by
-  simp only [Pmf.bind_pure, Pmf.bindOnSupport_eq_bind]
-#align pmf.bind_on_support_pure Pmf.bindOnSupport_pure
+#print PMF.bindOnSupport_pure /-
+theorem bindOnSupport_pure (p : PMF α) : (p.bindOnSupport fun a _ => pure a) = p := by
+  simp only [PMF.bind_pure, PMF.bindOnSupport_eq_bind]
+#align pmf.bind_on_support_pure PMF.bindOnSupport_pure
 -/
 
-#print Pmf.bindOnSupport_bindOnSupport /-
+#print PMF.bindOnSupport_bindOnSupport /-
 @[simp]
-theorem bindOnSupport_bindOnSupport (p : Pmf α) (f : ∀ a ∈ p.support, Pmf β)
-    (g : ∀ b ∈ (p.bindOnSupport f).support, Pmf γ) :
+theorem bindOnSupport_bindOnSupport (p : PMF α) (f : ∀ a ∈ p.support, PMF β)
+    (g : ∀ b ∈ (p.bindOnSupport f).support, PMF γ) :
     (p.bindOnSupport f).bindOnSupport g =
       p.bindOnSupport fun a ha =>
         (f a ha).bindOnSupport fun b hb =>
           g b ((mem_support_bindOnSupport_iff f b).mpr ⟨a, ha, hb⟩) :=
   by
-  refine' Pmf.ext fun a => _
+  refine' PMF.ext fun a => _
   simp only [ennreal.coe_eq_coe.symm, bind_on_support_apply, ← tsum_dite_right,
     ennreal.tsum_mul_left.symm, ennreal.tsum_mul_right.symm]
   simp only [ENNReal.tsum_eq_zero, ENNReal.coe_eq_coe, ENNReal.coe_eq_zero, ENNReal.coe_zero,
@@ -364,20 +364,20 @@ theorem bindOnSupport_bindOnSupport (p : Pmf α) (f : ∀ a ∈ p.support, Pmf 
   any_goals ring1
   · have := h_1 a'; simp [h] at this ; contradiction
   · simp [h_2]
-#align pmf.bind_on_support_bind_on_support Pmf.bindOnSupport_bindOnSupport
+#align pmf.bind_on_support_bind_on_support PMF.bindOnSupport_bindOnSupport
 -/
 
-#print Pmf.bindOnSupport_comm /-
-theorem bindOnSupport_comm (p : Pmf α) (q : Pmf β) (f : ∀ a ∈ p.support, ∀ b ∈ q.support, Pmf γ) :
+#print PMF.bindOnSupport_comm /-
+theorem bindOnSupport_comm (p : PMF α) (q : PMF β) (f : ∀ a ∈ p.support, ∀ b ∈ q.support, PMF γ) :
     (p.bindOnSupport fun a ha => q.bindOnSupport (f a ha)) =
       q.bindOnSupport fun b hb => p.bindOnSupport fun a ha => f a ha b hb :=
   by
-  apply Pmf.ext; rintro c
+  apply PMF.ext; rintro c
   simp only [ennreal.coe_eq_coe.symm, bind_on_support_apply, ← tsum_dite_right,
     ennreal.tsum_mul_left.symm, ennreal.tsum_mul_right.symm]
   refine' trans ENNReal.tsum_comm (tsum_congr fun b => tsum_congr fun a => _)
   split_ifs with h1 h2 h2 <;> ring
-#align pmf.bind_on_support_comm Pmf.bindOnSupport_comm
+#align pmf.bind_on_support_comm PMF.bindOnSupport_comm
 -/
 
 section Measure
@@ -386,7 +386,7 @@ variable (s : Set β)
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (a b) -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (b a) -/
-#print Pmf.toOuterMeasure_bindOnSupport_apply /-
+#print PMF.toOuterMeasure_bindOnSupport_apply /-
 @[simp]
 theorem toOuterMeasure_bindOnSupport_apply :
     (p.bindOnSupport f).toOuterMeasure s =
@@ -403,10 +403,10 @@ theorem toOuterMeasure_bindOnSupport_apply :
       (tsum_congr fun a => by simp only [← ENNReal.tsum_mul_left, mul_ite, MulZeroClass.mul_zero])
     _ = ∑' a, p a * dite (p a = 0) (fun h => 0) fun h => ∑' b, ite (b ∈ s) (f a h b) 0 :=
       tsum_congr fun a => by split_ifs with ha <;> simp only [if_t_t, tsum_zero, eq_self_iff_true]
-#align pmf.to_outer_measure_bind_on_support_apply Pmf.toOuterMeasure_bindOnSupport_apply
+#align pmf.to_outer_measure_bind_on_support_apply PMF.toOuterMeasure_bindOnSupport_apply
 -/
 
-#print Pmf.toMeasure_bindOnSupport_apply /-
+#print PMF.toMeasure_bindOnSupport_apply /-
 /-- The measure of a set under `p.bind_on_support f` is the sum over `a : α`
   of the probability of `a` under `p` times the measure of the set under `f a _`.
   The additional if statement is needed since `f` is only a partial function -/
@@ -416,12 +416,12 @@ theorem toMeasure_bindOnSupport_apply [MeasurableSpace β] (hs : MeasurableSet s
   by
   simp only [to_measure_apply_eq_to_outer_measure_apply _ _ hs,
     to_outer_measure_bind_on_support_apply]
-#align pmf.to_measure_bind_on_support_apply Pmf.toMeasure_bindOnSupport_apply
+#align pmf.to_measure_bind_on_support_apply PMF.toMeasure_bindOnSupport_apply
 -/
 
 end Measure
 
 end BindOnSupport
 
-end Pmf
+end PMF
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451

@@ -3,7 +3,7 @@ Copyright (c) 2020 Devon Tuma. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Devon Tuma
 -/
-import Mathbin.Probability.ProbabilityMassFunction.Basic
+import Probability.ProbabilityMassFunction.Basic
 
 #align_import probability.probability_mass_function.monad from "leanprover-community/mathlib"@"bd15ff41b70f5e2cc210f26f25a8d5c53b20d3de"
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345

@@ -2,14 +2,11 @@
 Copyright (c) 2020 Devon Tuma. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Devon Tuma
-
-! This file was ported from Lean 3 source module probability.probability_mass_function.monad
-! leanprover-community/mathlib commit bd15ff41b70f5e2cc210f26f25a8d5c53b20d3de
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Probability.ProbabilityMassFunction.Basic
 
+#align_import probability.probability_mass_function.monad from "leanprover-community/mathlib"@"bd15ff41b70f5e2cc210f26f25a8d5c53b20d3de"
+
 /-!
 # Monad Operations for Probability Mass Functions
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/2a0ce625dbb0ffbc7d1316597de0b25c1ec75303

@@ -313,7 +313,7 @@ theorem mem_support_bindOnSupport_iff (b : β) :
 theorem bindOnSupport_eq_bind (p : Pmf α) (f : α → Pmf β) :
     (p.bindOnSupport fun a _ => f a) = p.bind f :=
   by
-  ext (b x)
+  ext b x
   have : ∀ a, ite (p a = 0) 0 (p a * f a b) = p a * f a b := fun a =>
     ite_eq_right_iff.2 fun h => h.symm ▸ symm (MulZeroClass.zero_mul <| f a b)
   simp only [bind_on_support_apply fun a _ => f a, p.bind_apply f, dite_eq_ite, mul_ite,

mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423

@@ -49,10 +49,12 @@ def pure (a : α) : Pmf α :=
 
 variable (a a' : α)
 
+#print Pmf.pure_apply /-
 @[simp]
 theorem pure_apply : pure a a' = if a' = a then 1 else 0 :=
   rfl
 #align pmf.pure_apply Pmf.pure_apply
+-/
 
 #print Pmf.support_pure /-
 @[simp]
@@ -73,9 +75,11 @@ theorem pure_apply_self : pure a a = 1 :=
 #align pmf.pure_apply_self Pmf.pure_apply_self
 -/
 
+#print Pmf.pure_apply_of_ne /-
 theorem pure_apply_of_ne (h : a' ≠ a) : pure a a' = 0 :=
   if_neg h
 #align pmf.pure_apply_of_ne Pmf.pure_apply_of_ne
+-/
 
 instance [Inhabited α] : Inhabited (Pmf α) :=
   ⟨pure default⟩
@@ -84,6 +88,7 @@ section Measure
 
 variable (s : Set α)
 
+#print Pmf.toOuterMeasure_pure_apply /-
 @[simp]
 theorem toOuterMeasure_pure_apply : (pure a).toOuterMeasure s = if a ∈ s then 1 else 0 :=
   by
@@ -94,15 +99,18 @@ theorem toOuterMeasure_pure_apply : (pure a).toOuterMeasure s = if a ∈ s then
   · refine' (tsum_congr fun b => _).trans tsum_zero
     exact ite_eq_right_iff.2 fun hb => ite_eq_right_iff.2 fun h => (ha <| h ▸ hb).elim
 #align pmf.to_outer_measure_pure_apply Pmf.toOuterMeasure_pure_apply
+-/
 
 variable [MeasurableSpace α]
 
+#print Pmf.toMeasure_pure_apply /-
 /-- The measure of a set under `pure a` is `1` for sets containing `a` and `0` otherwise -/
 @[simp]
 theorem toMeasure_pure_apply (hs : MeasurableSet s) :
     (pure a).toMeasure s = if a ∈ s then 1 else 0 :=
   (toMeasure_apply_eq_toOuterMeasure_apply (pure a) s hs).trans (toOuterMeasure_pure_apply a s)
 #align pmf.to_measure_pure_apply Pmf.toMeasure_pure_apply
+-/
 
 #print Pmf.toMeasure_pure /-
 theorem toMeasure_pure : (pure a).toMeasure = Measure.dirac a :=
@@ -134,10 +142,12 @@ def bind (p : Pmf α) (f : α → Pmf β) : Pmf β :=
 
 variable (p : Pmf α) (f : α → Pmf β) (g : β → Pmf γ)
 
+#print Pmf.bind_apply /-
 @[simp]
 theorem bind_apply (b : β) : p.bind f b = ∑' a, p a * f a b :=
   rfl
 #align pmf.bind_apply Pmf.bind_apply
+-/
 
 #print Pmf.support_bind /-
 @[simp]
@@ -146,10 +156,12 @@ theorem support_bind : (p.bind f).support = ⋃ a ∈ p.support, (f a).support :
 #align pmf.support_bind Pmf.support_bind
 -/
 
+#print Pmf.mem_support_bind_iff /-
 theorem mem_support_bind_iff (b : β) :
     b ∈ (p.bind f).support ↔ ∃ a ∈ p.support, b ∈ (f a).support := by
   simp only [support_bind, Set.mem_iUnion, Set.mem_setOf_eq]
 #align pmf.mem_support_bind_iff Pmf.mem_support_bind_iff
+-/
 
 #print Pmf.pure_bind /-
 @[simp]
@@ -173,10 +185,12 @@ theorem bind_pure : p.bind pure = p :=
 #align pmf.bind_pure Pmf.bind_pure
 -/
 
+#print Pmf.bind_const /-
 @[simp]
 theorem bind_const (p : Pmf α) (q : Pmf β) : (p.bind fun _ => q) = q :=
   Pmf.ext fun x => by rw [bind_apply, ENNReal.tsum_mul_right, tsum_coe, one_mul]
 #align pmf.bind_const Pmf.bind_const
+-/
 
 #print Pmf.bind_bind /-
 @[simp]
@@ -187,12 +201,14 @@ theorem bind_bind : (p.bind f).bind g = p.bind fun a => (f a).bind g :=
 #align pmf.bind_bind Pmf.bind_bind
 -/
 
+#print Pmf.bind_comm /-
 theorem bind_comm (p : Pmf α) (q : Pmf β) (f : α → β → Pmf γ) :
     (p.bind fun a => q.bind (f a)) = q.bind fun b => p.bind fun a => f a b :=
   Pmf.ext fun b => by
     simpa only [ennreal.coe_eq_coe.symm, bind_apply, ennreal.tsum_mul_left.symm,
       ennreal.tsum_mul_right.symm, mul_assoc, mul_left_comm, mul_comm] using ENNReal.tsum_comm
 #align pmf.bind_comm Pmf.bind_comm
+-/
 
 section Measure
 
@@ -200,6 +216,7 @@ variable (s : Set β)
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (b a) -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (a b) -/
+#print Pmf.toOuterMeasure_bind_apply /-
 @[simp]
 theorem toOuterMeasure_bind_apply :
     (p.bind f).toOuterMeasure s = ∑' a, p a * (f a).toOuterMeasure s :=
@@ -215,7 +232,9 @@ theorem toOuterMeasure_bind_apply :
     _ = ∑' a, p a * (f a).toOuterMeasure s :=
       tsum_congr fun a => by simp only [to_outer_measure_apply, Set.indicator_apply]
 #align pmf.to_outer_measure_bind_apply Pmf.toOuterMeasure_bind_apply
+-/
 
+#print Pmf.toMeasure_bind_apply /-
 /-- The measure of a set under `p.bind f` is the sum over `a : α`
   of the probability of `a` under `p` times the measure of the set under `f a` -/
 @[simp]
@@ -226,6 +245,7 @@ theorem toMeasure_bind_apply [MeasurableSpace β] (hs : MeasurableSet s) :
       (tsum_congr fun a =>
         congr_arg (fun x => p a * x) (toMeasure_apply_eq_toOuterMeasure_apply (f a) s hs).symm))
 #align pmf.to_measure_bind_apply Pmf.toMeasure_bind_apply
+-/
 
 end Measure
 
@@ -254,11 +274,13 @@ def bindOnSupport (p : Pmf α) (f : ∀ a ∈ p.support, Pmf β) : Pmf β :=
 
 variable {p : Pmf α} (f : ∀ a ∈ p.support, Pmf β)
 
+#print Pmf.bindOnSupport_apply /-
 @[simp]
 theorem bindOnSupport_apply (b : β) :
     p.bindOnSupport f b = ∑' a, p a * if h : p a = 0 then 0 else f a h b :=
   rfl
 #align pmf.bind_on_support_apply Pmf.bindOnSupport_apply
+-/
 
 #print Pmf.support_bindOnSupport /-
 @[simp]
@@ -285,6 +307,7 @@ theorem mem_support_bindOnSupport_iff (b : β) :
 #align pmf.mem_support_bind_on_support_iff Pmf.mem_support_bindOnSupport_iff
 -/
 
+#print Pmf.bindOnSupport_eq_bind /-
 /-- `bind_on_support` reduces to `bind` if `f` doesn't depend on the additional hypothesis -/
 @[simp]
 theorem bindOnSupport_eq_bind (p : Pmf α) (f : α → Pmf β) :
@@ -296,14 +319,18 @@ theorem bindOnSupport_eq_bind (p : Pmf α) (f : α → Pmf β) :
   simp only [bind_on_support_apply fun a _ => f a, p.bind_apply f, dite_eq_ite, mul_ite,
     MulZeroClass.mul_zero, this]
 #align pmf.bind_on_support_eq_bind Pmf.bindOnSupport_eq_bind
+-/
 
+#print Pmf.bindOnSupport_eq_zero_iff /-
 theorem bindOnSupport_eq_zero_iff (b : β) :
     p.bindOnSupport f b = 0 ↔ ∀ (a) (ha : p a ≠ 0), f a ha b = 0 :=
   by
   simp only [bind_on_support_apply, ENNReal.tsum_eq_zero, mul_eq_zero, or_iff_not_imp_left]
   exact ⟨fun h a ha => trans (dif_neg ha).symm (h a ha), fun h a ha => trans (dif_neg ha) (h a ha)⟩
 #align pmf.bind_on_support_eq_zero_iff Pmf.bindOnSupport_eq_zero_iff
+-/
 
+#print Pmf.pure_bindOnSupport /-
 @[simp]
 theorem pure_bindOnSupport (a : α) (f : ∀ (a' : α) (ha : a' ∈ (pure a).support), Pmf β) :
     (pure a).bindOnSupport f = f a ((mem_support_pure_iff a a).mpr rfl) :=
@@ -313,6 +340,7 @@ theorem pure_bindOnSupport (a : α) (f : ∀ (a' : α) (ha : a' ∈ (pure a).sup
   refine' trans (tsum_congr fun a' => _) (tsum_ite_eq a _)
   by_cases h : a' = a <;> simp [h]
 #align pmf.pure_bind_on_support Pmf.pure_bindOnSupport
+-/
 
 #print Pmf.bindOnSupport_pure /-
 theorem bindOnSupport_pure (p : Pmf α) : (p.bindOnSupport fun a _ => pure a) = p := by
@@ -320,6 +348,7 @@ theorem bindOnSupport_pure (p : Pmf α) : (p.bindOnSupport fun a _ => pure a) =
 #align pmf.bind_on_support_pure Pmf.bindOnSupport_pure
 -/
 
+#print Pmf.bindOnSupport_bindOnSupport /-
 @[simp]
 theorem bindOnSupport_bindOnSupport (p : Pmf α) (f : ∀ a ∈ p.support, Pmf β)
     (g : ∀ b ∈ (p.bindOnSupport f).support, Pmf γ) :
@@ -339,7 +368,9 @@ theorem bindOnSupport_bindOnSupport (p : Pmf α) (f : ∀ a ∈ p.support, Pmf 
   · have := h_1 a'; simp [h] at this ; contradiction
   · simp [h_2]
 #align pmf.bind_on_support_bind_on_support Pmf.bindOnSupport_bindOnSupport
+-/
 
+#print Pmf.bindOnSupport_comm /-
 theorem bindOnSupport_comm (p : Pmf α) (q : Pmf β) (f : ∀ a ∈ p.support, ∀ b ∈ q.support, Pmf γ) :
     (p.bindOnSupport fun a ha => q.bindOnSupport (f a ha)) =
       q.bindOnSupport fun b hb => p.bindOnSupport fun a ha => f a ha b hb :=
@@ -350,6 +381,7 @@ theorem bindOnSupport_comm (p : Pmf α) (q : Pmf β) (f : ∀ a ∈ p.support, 
   refine' trans ENNReal.tsum_comm (tsum_congr fun b => tsum_congr fun a => _)
   split_ifs with h1 h2 h2 <;> ring
 #align pmf.bind_on_support_comm Pmf.bindOnSupport_comm
+-/
 
 section Measure
 
@@ -357,6 +389,7 @@ variable (s : Set β)
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (a b) -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (b a) -/
+#print Pmf.toOuterMeasure_bindOnSupport_apply /-
 @[simp]
 theorem toOuterMeasure_bindOnSupport_apply :
     (p.bindOnSupport f).toOuterMeasure s =
@@ -374,7 +407,9 @@ theorem toOuterMeasure_bindOnSupport_apply :
     _ = ∑' a, p a * dite (p a = 0) (fun h => 0) fun h => ∑' b, ite (b ∈ s) (f a h b) 0 :=
       tsum_congr fun a => by split_ifs with ha <;> simp only [if_t_t, tsum_zero, eq_self_iff_true]
 #align pmf.to_outer_measure_bind_on_support_apply Pmf.toOuterMeasure_bindOnSupport_apply
+-/
 
+#print Pmf.toMeasure_bindOnSupport_apply /-
 /-- The measure of a set under `p.bind_on_support f` is the sum over `a : α`
   of the probability of `a` under `p` times the measure of the set under `f a _`.
   The additional if statement is needed since `f` is only a partial function -/
@@ -385,6 +420,7 @@ theorem toMeasure_bindOnSupport_apply [MeasurableSpace β] (hs : MeasurableSet s
   simp only [to_measure_apply_eq_to_outer_measure_apply _ _ hs,
     to_outer_measure_bind_on_support_apply]
 #align pmf.to_measure_bind_on_support_apply Pmf.toMeasure_bindOnSupport_apply
+-/
 
 end Measure
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/a3e83f0fa4391c8740f7d773a7a9b74e311ae2a3

@@ -364,7 +364,7 @@ theorem toOuterMeasure_bindOnSupport_apply :
   by
   simp only [to_outer_measure_apply, Set.indicator_apply, bind_on_support_apply]
   calc
-    (∑' b, ite (b ∈ s) (∑' a, p a * dite (p a = 0) (fun h => 0) fun h => f a h b) 0) =
+    ∑' b, ite (b ∈ s) (∑' a, p a * dite (p a = 0) (fun h => 0) fun h => f a h b) 0 =
         ∑' (b) (a), ite (b ∈ s) (p a * dite (p a = 0) (fun h => 0) fun h => f a h b) 0 :=
       tsum_congr fun b => by split_ifs with hbs <;> simp only [eq_self_iff_true, tsum_zero]
     _ = ∑' (a) (b), ite (b ∈ s) (p a * dite (p a = 0) (fun h => 0) fun h => f a h b) 0 :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/7e5137f579de09a059a5ce98f364a04e221aabf0

@@ -214,7 +214,6 @@ theorem toOuterMeasure_bind_apply :
       (tsum_congr fun a => (congr_arg fun x => p a * x) <| tsum_congr fun b => by split_ifs <;> rfl)
     _ = ∑' a, p a * (f a).toOuterMeasure s :=
       tsum_congr fun a => by simp only [to_outer_measure_apply, Set.indicator_apply]
-    
 #align pmf.to_outer_measure_bind_apply Pmf.toOuterMeasure_bind_apply
 
 /-- The measure of a set under `p.bind f` is the sum over `a : α`
@@ -374,7 +373,6 @@ theorem toOuterMeasure_bindOnSupport_apply :
       (tsum_congr fun a => by simp only [← ENNReal.tsum_mul_left, mul_ite, MulZeroClass.mul_zero])
     _ = ∑' a, p a * dite (p a = 0) (fun h => 0) fun h => ∑' b, ite (b ∈ s) (f a h b) 0 :=
       tsum_congr fun a => by split_ifs with ha <;> simp only [if_t_t, tsum_zero, eq_self_iff_true]
-    
 #align pmf.to_outer_measure_bind_on_support_apply Pmf.toOuterMeasure_bindOnSupport_apply
 
 /-- The measure of a set under `p.bind_on_support f` is the sum over `a : α`

mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb

@@ -281,7 +281,7 @@ theorem support_bindOnSupport :
 
 #print Pmf.mem_support_bindOnSupport_iff /-
 theorem mem_support_bindOnSupport_iff (b : β) :
-    b ∈ (p.bindOnSupport f).support ↔ ∃ (a : α)(h : a ∈ p.support), b ∈ (f a h).support := by
+    b ∈ (p.bindOnSupport f).support ↔ ∃ (a : α) (h : a ∈ p.support), b ∈ (f a h).support := by
   simp only [support_bind_on_support, Set.mem_setOf_eq, Set.mem_iUnion]
 #align pmf.mem_support_bind_on_support_iff Pmf.mem_support_bindOnSupport_iff
 -/
@@ -337,7 +337,7 @@ theorem bindOnSupport_bindOnSupport (p : Pmf α) (f : ∀ a ∈ p.support, Pmf 
   refine' ennreal.tsum_comm.trans (tsum_congr fun a' => tsum_congr fun b => _)
   split_ifs
   any_goals ring1
-  · have := h_1 a'; simp [h] at this; contradiction
+  · have := h_1 a'; simp [h] at this ; contradiction
   · simp [h_2]
 #align pmf.bind_on_support_bind_on_support Pmf.bindOnSupport_bindOnSupport
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

@@ -31,7 +31,7 @@ noncomputable section
 
 variable {α β γ : Type _}
 
-open Classical BigOperators NNReal ENNReal
+open scoped Classical BigOperators NNReal ENNReal
 
 open MeasureTheory
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

@@ -49,12 +49,6 @@ def pure (a : α) : Pmf α :=
 
 variable (a a' : α)
 
-/- warning: pmf.pure_apply -> Pmf.pure_apply is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} (a : α) (a' : α), Eq.{1} ENNReal (coeFn.{succ u1, succ u1} (Pmf.{u1} α) (fun (_x : Pmf.{u1} α) => α -> ENNReal) (FunLike.hasCoeToFun.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (p : α) => ENNReal) (Pmf.funLike.{u1} α)) (Pmf.pure.{u1} α a) a') (ite.{1} ENNReal (Eq.{succ u1} α a' a) (Classical.propDecidable (Eq.{succ u1} α a' a)) (OfNat.ofNat.{0} ENNReal 1 (OfNat.mk.{0} ENNReal 1 (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))))
-but is expected to have type
-  forall {α : Type.{u1}} (a : α) (a' : α), Eq.{1} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a') (FunLike.coe.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (_x : α) => (fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) _x) (Pmf.funLike.{u1} α) (Pmf.pure.{u1} α a) a') (ite.{1} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a') (Eq.{succ u1} α a' a) (Classical.propDecidable (Eq.{succ u1} α a' a)) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a') 1 (One.toOfNat1.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a') (CanonicallyOrderedCommSemiring.toOne.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a') ENNReal.instCanonicallyOrderedCommSemiringENNReal))) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a') 0 (Zero.toOfNat0.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a') instENNRealZero)))
-Case conversion may be inaccurate. Consider using '#align pmf.pure_apply Pmf.pure_applyₓ'. -/
 @[simp]
 theorem pure_apply : pure a a' = if a' = a then 1 else 0 :=
   rfl
@@ -79,12 +73,6 @@ theorem pure_apply_self : pure a a = 1 :=
 #align pmf.pure_apply_self Pmf.pure_apply_self
 -/
 
-/- warning: pmf.pure_apply_of_ne -> Pmf.pure_apply_of_ne is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} (a : α) (a' : α), (Ne.{succ u1} α a' a) -> (Eq.{1} ENNReal (coeFn.{succ u1, succ u1} (Pmf.{u1} α) (fun (_x : Pmf.{u1} α) => α -> ENNReal) (FunLike.hasCoeToFun.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (p : α) => ENNReal) (Pmf.funLike.{u1} α)) (Pmf.pure.{u1} α a) a') (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))))
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align pmf.pure_apply_of_ne Pmf.pure_apply_of_neₓ'. -/
 theorem pure_apply_of_ne (h : a' ≠ a) : pure a a' = 0 :=
   if_neg h
 #align pmf.pure_apply_of_ne Pmf.pure_apply_of_ne
@@ -96,12 +84,6 @@ section Measure
 
 variable (s : Set α)
 
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 @[simp]
 theorem toOuterMeasure_pure_apply : (pure a).toOuterMeasure s = if a ∈ s then 1 else 0 :=
   by
@@ -115,12 +97,6 @@ theorem toOuterMeasure_pure_apply : (pure a).toOuterMeasure s = if a ∈ s then
 
 variable [MeasurableSpace α]
 
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 /-- The measure of a set under `pure a` is `1` for sets containing `a` and `0` otherwise -/
 @[simp]
 theorem toMeasure_pure_apply (hs : MeasurableSet s) :
@@ -158,12 +134,6 @@ def bind (p : Pmf α) (f : α → Pmf β) : Pmf β :=
 
 variable (p : Pmf α) (f : α → Pmf β) (g : β → Pmf γ)
 
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 @[simp]
 theorem bind_apply (b : β) : p.bind f b = ∑' a, p a * f a b :=
   rfl
@@ -176,12 +146,6 @@ theorem support_bind : (p.bind f).support = ⋃ a ∈ p.support, (f a).support :
 #align pmf.support_bind Pmf.support_bind
 -/
 
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 theorem mem_support_bind_iff (b : β) :
     b ∈ (p.bind f).support ↔ ∃ a ∈ p.support, b ∈ (f a).support := by
   simp only [support_bind, Set.mem_iUnion, Set.mem_setOf_eq]
@@ -209,12 +173,6 @@ theorem bind_pure : p.bind pure = p :=
 #align pmf.bind_pure Pmf.bind_pure
 -/
 
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 @[simp]
 theorem bind_const (p : Pmf α) (q : Pmf β) : (p.bind fun _ => q) = q :=
   Pmf.ext fun x => by rw [bind_apply, ENNReal.tsum_mul_right, tsum_coe, one_mul]
@@ -229,12 +187,6 @@ theorem bind_bind : (p.bind f).bind g = p.bind fun a => (f a).bind g :=
 #align pmf.bind_bind Pmf.bind_bind
 -/
 
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 theorem bind_comm (p : Pmf α) (q : Pmf β) (f : α → β → Pmf γ) :
     (p.bind fun a => q.bind (f a)) = q.bind fun b => p.bind fun a => f a b :=
   Pmf.ext fun b => by
@@ -246,12 +198,6 @@ section Measure
 
 variable (s : Set β)
 
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 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (b a) -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (a b) -/
 @[simp]
@@ -271,12 +217,6 @@ theorem toOuterMeasure_bind_apply :
     
 #align pmf.to_outer_measure_bind_apply Pmf.toOuterMeasure_bind_apply
 
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 /-- The measure of a set under `p.bind f` is the sum over `a : α`
   of the probability of `a` under `p` times the measure of the set under `f a` -/
 @[simp]
@@ -315,12 +255,6 @@ def bindOnSupport (p : Pmf α) (f : ∀ a ∈ p.support, Pmf β) : Pmf β :=
 
 variable {p : Pmf α} (f : ∀ a ∈ p.support, Pmf β)
 
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 @[simp]
 theorem bindOnSupport_apply (b : β) :
     p.bindOnSupport f b = ∑' a, p a * if h : p a = 0 then 0 else f a h b :=
@@ -352,12 +286,6 @@ theorem mem_support_bindOnSupport_iff (b : β) :
 #align pmf.mem_support_bind_on_support_iff Pmf.mem_support_bindOnSupport_iff
 -/
 
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 /-- `bind_on_support` reduces to `bind` if `f` doesn't depend on the additional hypothesis -/
 @[simp]
 theorem bindOnSupport_eq_bind (p : Pmf α) (f : α → Pmf β) :
@@ -370,12 +298,6 @@ theorem bindOnSupport_eq_bind (p : Pmf α) (f : α → Pmf β) :
     MulZeroClass.mul_zero, this]
 #align pmf.bind_on_support_eq_bind Pmf.bindOnSupport_eq_bind
 
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 theorem bindOnSupport_eq_zero_iff (b : β) :
     p.bindOnSupport f b = 0 ↔ ∀ (a) (ha : p a ≠ 0), f a ha b = 0 :=
   by
@@ -383,12 +305,6 @@ theorem bindOnSupport_eq_zero_iff (b : β) :
   exact ⟨fun h a ha => trans (dif_neg ha).symm (h a ha), fun h a ha => trans (dif_neg ha) (h a ha)⟩
 #align pmf.bind_on_support_eq_zero_iff Pmf.bindOnSupport_eq_zero_iff
 
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 @[simp]
 theorem pure_bindOnSupport (a : α) (f : ∀ (a' : α) (ha : a' ∈ (pure a).support), Pmf β) :
     (pure a).bindOnSupport f = f a ((mem_support_pure_iff a a).mpr rfl) :=
@@ -405,12 +321,6 @@ theorem bindOnSupport_pure (p : Pmf α) : (p.bindOnSupport fun a _ => pure a) =
 #align pmf.bind_on_support_pure Pmf.bindOnSupport_pure
 -/
 
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-Case conversion may be inaccurate. Consider using '#align pmf.bind_on_support_bind_on_support Pmf.bindOnSupport_bindOnSupportₓ'. -/
 @[simp]
 theorem bindOnSupport_bindOnSupport (p : Pmf α) (f : ∀ a ∈ p.support, Pmf β)
     (g : ∀ b ∈ (p.bindOnSupport f).support, Pmf γ) :
@@ -431,12 +341,6 @@ theorem bindOnSupport_bindOnSupport (p : Pmf α) (f : ∀ a ∈ p.support, Pmf 
   · simp [h_2]
 #align pmf.bind_on_support_bind_on_support Pmf.bindOnSupport_bindOnSupport
 
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-Case conversion may be inaccurate. Consider using '#align pmf.bind_on_support_comm Pmf.bindOnSupport_commₓ'. -/
 theorem bindOnSupport_comm (p : Pmf α) (q : Pmf β) (f : ∀ a ∈ p.support, ∀ b ∈ q.support, Pmf γ) :
     (p.bindOnSupport fun a ha => q.bindOnSupport (f a ha)) =
       q.bindOnSupport fun b hb => p.bindOnSupport fun a ha => f a ha b hb :=
@@ -452,12 +356,6 @@ section Measure
 
 variable (s : Set β)
 
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-Case conversion may be inaccurate. Consider using '#align pmf.to_outer_measure_bind_on_support_apply Pmf.toOuterMeasure_bindOnSupport_applyₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (a b) -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (b a) -/
 @[simp]
@@ -479,12 +377,6 @@ theorem toOuterMeasure_bindOnSupport_apply :
     
 #align pmf.to_outer_measure_bind_on_support_apply Pmf.toOuterMeasure_bindOnSupport_apply
 
-/- warning: pmf.to_measure_bind_on_support_apply -> Pmf.toMeasure_bindOnSupport_apply is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {p : Pmf.{u1} α} (f : forall (a : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a (Pmf.support.{u1} α p)) -> (Pmf.{u2} β)) (s : Set.{u2} β) [_inst_1 : MeasurableSpace.{u2} β], (MeasurableSet.{u2} β _inst_1 s) -> (Eq.{1} ENNReal (coeFn.{succ u2, succ u2} (MeasureTheory.Measure.{u2} β _inst_1) (fun (_x : MeasureTheory.Measure.{u2} β _inst_1) => (Set.{u2} β) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u2} β _inst_1) (Pmf.toMeasure.{u2} β _inst_1 (Pmf.bindOnSupport.{u1, u2} α β p f)) s) (tsum.{0, u1} ENNReal (OrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))) ENNReal.topologicalSpace α (fun (a : α) => HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (Distrib.toHasMul.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (coeFn.{succ u1, succ u1} (Pmf.{u1} α) (fun (_x : Pmf.{u1} α) => α -> ENNReal) (FunLike.hasCoeToFun.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (p : α) => ENNReal) (Pmf.funLike.{u1} α)) p a) (dite.{1} ENNReal (Eq.{1} ENNReal (coeFn.{succ u1, succ u1} (Pmf.{u1} α) (fun (_x : Pmf.{u1} α) => α -> ENNReal) (FunLike.hasCoeToFun.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (p : α) => ENNReal) (Pmf.funLike.{u1} α)) p a) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (Option.decidableEq.{0} NNReal (fun (a : NNReal) (b : NNReal) => Subtype.decidableEq.{0} Real (fun (x : Real) => LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) x) (fun (a : Real) (b : Real) => Real.decidableEq a b) a b) (coeFn.{succ u1, succ u1} (Pmf.{u1} α) (fun (_x : Pmf.{u1} α) => α -> ENNReal) (FunLike.hasCoeToFun.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (p : α) => ENNReal) (Pmf.funLike.{u1} α)) p a) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (fun (h : Eq.{1} ENNReal (coeFn.{succ u1, succ u1} (Pmf.{u1} α) (fun (_x : Pmf.{u1} α) => α -> ENNReal) (FunLike.hasCoeToFun.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (p : α) => ENNReal) (Pmf.funLike.{u1} α)) p a) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) => OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) (fun (h : Not (Eq.{1} ENNReal (coeFn.{succ u1, succ u1} (Pmf.{u1} α) (fun (_x : Pmf.{u1} α) => α -> ENNReal) (FunLike.hasCoeToFun.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (p : α) => ENNReal) (Pmf.funLike.{u1} α)) p a) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))))) => coeFn.{succ u2, succ u2} (MeasureTheory.Measure.{u2} β _inst_1) (fun (_x : MeasureTheory.Measure.{u2} β _inst_1) => (Set.{u2} β) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u2} β _inst_1) (Pmf.toMeasure.{u2} β _inst_1 (f a h)) s)))))
-but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} {p : Pmf.{u1} α} (f : forall (a : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a (Pmf.support.{u1} α p)) -> (Pmf.{u2} β)) (s : Set.{u2} β) [_inst_1 : MeasurableSpace.{u2} β], (MeasurableSet.{u2} β _inst_1 s) -> (Eq.{1} ENNReal (MeasureTheory.OuterMeasure.measureOf.{u2} β (MeasureTheory.Measure.toOuterMeasure.{u2} β _inst_1 (Pmf.toMeasure.{u2} β _inst_1 (Pmf.bindOnSupport.{u1, u2} α β p f))) s) (tsum.{0, u1} ENNReal (LinearOrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (LinearOrderedAddCommMonoidWithTop.toLinearOrderedAddCommMonoid.{0} ENNReal ENNReal.instLinearOrderedAddCommMonoidWithTopENNReal)) ENNReal.instTopologicalSpaceENNReal α (fun (a : α) => HMul.hMul.{0, 0, 0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) ENNReal ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) (instHMul.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) (CanonicallyOrderedCommSemiring.toMul.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) ENNReal.instCanonicallyOrderedCommSemiringENNReal)) (FunLike.coe.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (_x : α) => (fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) _x) (Pmf.funLike.{u1} α) p a) (dite.{1} ENNReal (Eq.{1} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) (FunLike.coe.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (_x : α) => (fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) _x) (Pmf.funLike.{u1} α) p a) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) 0 (Zero.toOfNat0.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) instENNRealZero))) (instDecidableEq.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) (instLinearOrder.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) ENNReal.instCompleteLinearOrderENNReal))) (FunLike.coe.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (_x : α) => (fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) _x) (Pmf.funLike.{u1} α) p a) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) 0 (Zero.toOfNat0.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) instENNRealZero))) (fun (h : Eq.{1} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) (FunLike.coe.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (_x : α) => (fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) _x) (Pmf.funLike.{u1} α) p a) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) 0 (Zero.toOfNat0.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) instENNRealZero))) => OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) (fun (h : Not (Eq.{1} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) (FunLike.coe.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (_x : α) => (fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) _x) (Pmf.funLike.{u1} α) p a) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) 0 (Zero.toOfNat0.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) instENNRealZero)))) => MeasureTheory.OuterMeasure.measureOf.{u2} β (MeasureTheory.Measure.toOuterMeasure.{u2} β _inst_1 (Pmf.toMeasure.{u2} β _inst_1 (f a h))) s)))))
-Case conversion may be inaccurate. Consider using '#align pmf.to_measure_bind_on_support_apply Pmf.toMeasure_bindOnSupport_applyₓ'. -/
 /-- The measure of a set under `p.bind_on_support f` is the sum over `a : α`
   of the probability of `a` under `p` times the measure of the set under `f a _`.
   The additional if statement is needed since `f` is only a partial function -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

@@ -427,9 +427,7 @@ theorem bindOnSupport_bindOnSupport (p : Pmf α) (f : ∀ a ∈ p.support, Pmf 
   refine' ennreal.tsum_comm.trans (tsum_congr fun a' => tsum_congr fun b => _)
   split_ifs
   any_goals ring1
-  · have := h_1 a'
-    simp [h] at this
-    contradiction
+  · have := h_1 a'; simp [h] at this; contradiction
   · simp [h_2]
 #align pmf.bind_on_support_bind_on_support Pmf.bindOnSupport_bindOnSupport
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/e3fb84046afd187b710170887195d50bada934ee

@@ -184,7 +184,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align pmf.mem_support_bind_iff Pmf.mem_support_bind_iffₓ'. -/
 theorem mem_support_bind_iff (b : β) :
     b ∈ (p.bind f).support ↔ ∃ a ∈ p.support, b ∈ (f a).support := by
-  simp only [support_bind, Set.mem_unionᵢ, Set.mem_setOf_eq]
+  simp only [support_bind, Set.mem_iUnion, Set.mem_setOf_eq]
 #align pmf.mem_support_bind_iff Pmf.mem_support_bind_iff
 
 #print Pmf.pure_bind /-
@@ -334,7 +334,7 @@ theorem support_bindOnSupport :
   by
   refine' Set.ext fun b => _
   simp only [ENNReal.tsum_eq_zero, not_or, mem_support_iff, bind_on_support_apply, Ne.def,
-    not_forall, mul_eq_zero, Set.mem_unionᵢ]
+    not_forall, mul_eq_zero, Set.mem_iUnion]
   exact
     ⟨fun hb =>
       let ⟨a, ⟨ha, ha'⟩⟩ := hb
@@ -348,7 +348,7 @@ theorem support_bindOnSupport :
 #print Pmf.mem_support_bindOnSupport_iff /-
 theorem mem_support_bindOnSupport_iff (b : β) :
     b ∈ (p.bindOnSupport f).support ↔ ∃ (a : α)(h : a ∈ p.support), b ∈ (f a h).support := by
-  simp only [support_bind_on_support, Set.mem_setOf_eq, Set.mem_unionᵢ]
+  simp only [support_bind_on_support, Set.mem_setOf_eq, Set.mem_iUnion]
 #align pmf.mem_support_bind_on_support_iff Pmf.mem_support_bindOnSupport_iff
 -/
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/403190b5419b3f03f1a2893ad9352ca7f7d8bff6

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Devon Tuma
 
 ! This file was ported from Lean 3 source module probability.probability_mass_function.monad
-! leanprover-community/mathlib commit 4ac69b290818724c159de091daa3acd31da0ee6d
+! leanprover-community/mathlib commit bd15ff41b70f5e2cc210f26f25a8d5c53b20d3de
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -13,6 +13,9 @@ import Mathbin.Probability.ProbabilityMassFunction.Basic
 /-!
 # Monad Operations for Probability Mass Functions
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file constructs two operations on `pmf` that give it a monad structure.
 `pure a` is the distribution where a single value `a` has probability `1`.
 `bind pa pb : pmf β` is the distribution given by sampling `a : α` from `pa : pmf α`,

mathlib commit https://github.com/leanprover-community/mathlib/commit/28b2a92f2996d28e580450863c130955de0ed398

@@ -36,32 +36,52 @@ namespace Pmf
 
 section Pure
 
+#print Pmf.pure /-
 /-- The pure `pmf` is the `pmf` where all the mass lies in one point.
   The value of `pure a` is `1` at `a` and `0` elsewhere. -/
 def pure (a : α) : Pmf α :=
   ⟨fun a' => if a' = a then 1 else 0, hasSum_ite_eq _ _⟩
 #align pmf.pure Pmf.pure
+-/
 
 variable (a a' : α)
 
+/- warning: pmf.pure_apply -> Pmf.pure_apply is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} (a : α) (a' : α), Eq.{1} ENNReal (coeFn.{succ u1, succ u1} (Pmf.{u1} α) (fun (_x : Pmf.{u1} α) => α -> ENNReal) (FunLike.hasCoeToFun.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (p : α) => ENNReal) (Pmf.funLike.{u1} α)) (Pmf.pure.{u1} α a) a') (ite.{1} ENNReal (Eq.{succ u1} α a' a) (Classical.propDecidable (Eq.{succ u1} α a' a)) (OfNat.ofNat.{0} ENNReal 1 (OfNat.mk.{0} ENNReal 1 (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))))
+but is expected to have type
+  forall {α : Type.{u1}} (a : α) (a' : α), Eq.{1} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a') (FunLike.coe.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (_x : α) => (fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) _x) (Pmf.funLike.{u1} α) (Pmf.pure.{u1} α a) a') (ite.{1} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a') (Eq.{succ u1} α a' a) (Classical.propDecidable (Eq.{succ u1} α a' a)) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a') 1 (One.toOfNat1.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a') (CanonicallyOrderedCommSemiring.toOne.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a') ENNReal.instCanonicallyOrderedCommSemiringENNReal))) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a') 0 (Zero.toOfNat0.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a') instENNRealZero)))
+Case conversion may be inaccurate. Consider using '#align pmf.pure_apply Pmf.pure_applyₓ'. -/
 @[simp]
 theorem pure_apply : pure a a' = if a' = a then 1 else 0 :=
   rfl
 #align pmf.pure_apply Pmf.pure_apply
 
+#print Pmf.support_pure /-
 @[simp]
 theorem support_pure : (pure a).support = {a} :=
   Set.ext fun a' => by simp [mem_support_iff]
 #align pmf.support_pure Pmf.support_pure
+-/
 
+#print Pmf.mem_support_pure_iff /-
 theorem mem_support_pure_iff : a' ∈ (pure a).support ↔ a' = a := by simp
 #align pmf.mem_support_pure_iff Pmf.mem_support_pure_iff
+-/
 
+#print Pmf.pure_apply_self /-
 @[simp]
 theorem pure_apply_self : pure a a = 1 :=
   if_pos rfl
 #align pmf.pure_apply_self Pmf.pure_apply_self
+-/
 
+/- warning: pmf.pure_apply_of_ne -> Pmf.pure_apply_of_ne is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} (a : α) (a' : α), (Ne.{succ u1} α a' a) -> (Eq.{1} ENNReal (coeFn.{succ u1, succ u1} (Pmf.{u1} α) (fun (_x : Pmf.{u1} α) => α -> ENNReal) (FunLike.hasCoeToFun.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (p : α) => ENNReal) (Pmf.funLike.{u1} α)) (Pmf.pure.{u1} α a) a') (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))))
+but is expected to have type
+  forall {α : Type.{u1}} (a : α) (a' : α), (Ne.{succ u1} α a' a) -> (Eq.{1} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a') (FunLike.coe.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (_x : α) => (fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) _x) (Pmf.funLike.{u1} α) (Pmf.pure.{u1} α a) a') (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a') 0 (Zero.toOfNat0.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a') instENNRealZero)))
+Case conversion may be inaccurate. Consider using '#align pmf.pure_apply_of_ne Pmf.pure_apply_of_neₓ'. -/
 theorem pure_apply_of_ne (h : a' ≠ a) : pure a a' = 0 :=
   if_neg h
 #align pmf.pure_apply_of_ne Pmf.pure_apply_of_ne
@@ -73,6 +93,12 @@ section Measure
 
 variable (s : Set α)
 
+/- warning: pmf.to_outer_measure_pure_apply -> Pmf.toOuterMeasure_pure_apply is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} (a : α) (s : Set.{u1} α), Eq.{1} ENNReal (coeFn.{succ u1, succ u1} (MeasureTheory.OuterMeasure.{u1} α) (fun (_x : MeasureTheory.OuterMeasure.{u1} α) => (Set.{u1} α) -> ENNReal) (MeasureTheory.OuterMeasure.instCoeFun.{u1} α) (Pmf.toOuterMeasure.{u1} α (Pmf.pure.{u1} α a)) s) (ite.{1} ENNReal (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) (Classical.propDecidable (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s)) (OfNat.ofNat.{0} ENNReal 1 (OfNat.mk.{0} ENNReal 1 (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))))
+but is expected to have type
+  forall {α : Type.{u1}} (a : α) (s : Set.{u1} α), Eq.{1} ENNReal (MeasureTheory.OuterMeasure.measureOf.{u1} α (Pmf.toOuterMeasure.{u1} α (Pmf.pure.{u1} α a)) s) (ite.{1} ENNReal (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) (Classical.propDecidable (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s)) (OfNat.ofNat.{0} ENNReal 1 (One.toOfNat1.{0} ENNReal (CanonicallyOrderedCommSemiring.toOne.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)))
+Case conversion may be inaccurate. Consider using '#align pmf.to_outer_measure_pure_apply Pmf.toOuterMeasure_pure_applyₓ'. -/
 @[simp]
 theorem toOuterMeasure_pure_apply : (pure a).toOuterMeasure s = if a ∈ s then 1 else 0 :=
   by
@@ -86,6 +112,12 @@ theorem toOuterMeasure_pure_apply : (pure a).toOuterMeasure s = if a ∈ s then
 
 variable [MeasurableSpace α]
 
+/- warning: pmf.to_measure_pure_apply -> Pmf.toMeasure_pure_apply is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} (a : α) (s : Set.{u1} α) [_inst_1 : MeasurableSpace.{u1} α], (MeasurableSet.{u1} α _inst_1 s) -> (Eq.{1} ENNReal (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} α _inst_1) (fun (_x : MeasureTheory.Measure.{u1} α _inst_1) => (Set.{u1} α) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} α _inst_1) (Pmf.toMeasure.{u1} α _inst_1 (Pmf.pure.{u1} α a)) s) (ite.{1} ENNReal (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) (Classical.propDecidable (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s)) (OfNat.ofNat.{0} ENNReal 1 (OfNat.mk.{0} ENNReal 1 (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))))
+but is expected to have type
+  forall {α : Type.{u1}} (a : α) (s : Set.{u1} α) [_inst_1 : MeasurableSpace.{u1} α], (MeasurableSet.{u1} α _inst_1 s) -> (Eq.{1} ENNReal (MeasureTheory.OuterMeasure.measureOf.{u1} α (MeasureTheory.Measure.toOuterMeasure.{u1} α _inst_1 (Pmf.toMeasure.{u1} α _inst_1 (Pmf.pure.{u1} α a))) s) (ite.{1} ENNReal (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) (Classical.propDecidable (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s)) (OfNat.ofNat.{0} ENNReal 1 (One.toOfNat1.{0} ENNReal (CanonicallyOrderedCommSemiring.toOne.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))))
+Case conversion may be inaccurate. Consider using '#align pmf.to_measure_pure_apply Pmf.toMeasure_pure_applyₓ'. -/
 /-- The measure of a set under `pure a` is `1` for sets containing `a` and `0` otherwise -/
 @[simp]
 theorem toMeasure_pure_apply (hs : MeasurableSet s) :
@@ -93,14 +125,18 @@ theorem toMeasure_pure_apply (hs : MeasurableSet s) :
   (toMeasure_apply_eq_toOuterMeasure_apply (pure a) s hs).trans (toOuterMeasure_pure_apply a s)
 #align pmf.to_measure_pure_apply Pmf.toMeasure_pure_apply
 
+#print Pmf.toMeasure_pure /-
 theorem toMeasure_pure : (pure a).toMeasure = Measure.dirac a :=
   Measure.ext fun s hs => by simpa only [to_measure_pure_apply a s hs, measure.dirac_apply' a hs]
 #align pmf.to_measure_pure Pmf.toMeasure_pure
+-/
 
+#print Pmf.toPmf_dirac /-
 @[simp]
 theorem toPmf_dirac [Countable α] [h : MeasurableSingletonClass α] :
     (Measure.dirac a).toPmf = pure a := by rw [to_pmf_eq_iff_to_measure_eq, to_measure_pure]
 #align pmf.to_pmf_dirac Pmf.toPmf_dirac
+-/
 
 end Measure
 
@@ -108,30 +144,47 @@ end Pure
 
 section Bind
 
+#print Pmf.bind /-
 /-- The monadic bind operation for `pmf`. -/
 def bind (p : Pmf α) (f : α → Pmf β) : Pmf β :=
   ⟨fun b => ∑' a, p a * f a b,
     ENNReal.summable.hasSum_iff.2
       (ENNReal.tsum_comm.trans <| by simp only [ENNReal.tsum_mul_left, tsum_coe, mul_one])⟩
 #align pmf.bind Pmf.bind
+-/
 
 variable (p : Pmf α) (f : α → Pmf β) (g : β → Pmf γ)
 
+/- warning: pmf.bind_apply -> Pmf.bind_apply is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} (p : Pmf.{u1} α) (f : α -> (Pmf.{u2} β)) (b : β), Eq.{1} ENNReal (coeFn.{succ u2, succ u2} (Pmf.{u2} β) (fun (_x : Pmf.{u2} β) => β -> ENNReal) (FunLike.hasCoeToFun.{succ u2, succ u2, 1} (Pmf.{u2} β) β (fun (p : β) => ENNReal) (Pmf.funLike.{u2} β)) (Pmf.bind.{u1, u2} α β p f) b) (tsum.{0, u1} ENNReal (OrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))) ENNReal.topologicalSpace α (fun (a : α) => HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (Distrib.toHasMul.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (coeFn.{succ u1, succ u1} (Pmf.{u1} α) (fun (_x : Pmf.{u1} α) => α -> ENNReal) (FunLike.hasCoeToFun.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (p : α) => ENNReal) (Pmf.funLike.{u1} α)) p a) (coeFn.{succ u2, succ u2} (Pmf.{u2} β) (fun (_x : Pmf.{u2} β) => β -> ENNReal) (FunLike.hasCoeToFun.{succ u2, succ u2, 1} (Pmf.{u2} β) β (fun (p : β) => ENNReal) (Pmf.funLike.{u2} β)) (f a) b)))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} (p : Pmf.{u1} α) (f : α -> (Pmf.{u2} β)) (b : β), Eq.{1} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : β) => ENNReal) b) (FunLike.coe.{succ u2, succ u2, 1} (Pmf.{u2} β) β (fun (_x : β) => (fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : β) => ENNReal) _x) (Pmf.funLike.{u2} β) (Pmf.bind.{u1, u2} α β p f) b) (tsum.{0, u1} ENNReal (LinearOrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (LinearOrderedAddCommMonoidWithTop.toLinearOrderedAddCommMonoid.{0} ENNReal ENNReal.instLinearOrderedAddCommMonoidWithTopENNReal)) ENNReal.instTopologicalSpaceENNReal α (fun (a : α) => HMul.hMul.{0, 0, 0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : β) => ENNReal) b) ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) (instHMul.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) (CanonicallyOrderedCommSemiring.toMul.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) ENNReal.instCanonicallyOrderedCommSemiringENNReal)) (FunLike.coe.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (_x : α) => (fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) _x) (Pmf.funLike.{u1} α) p a) (FunLike.coe.{succ u2, succ u2, 1} (Pmf.{u2} β) β (fun (_x : β) => (fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : β) => ENNReal) _x) (Pmf.funLike.{u2} β) (f a) b)))
+Case conversion may be inaccurate. Consider using '#align pmf.bind_apply Pmf.bind_applyₓ'. -/
 @[simp]
 theorem bind_apply (b : β) : p.bind f b = ∑' a, p a * f a b :=
   rfl
 #align pmf.bind_apply Pmf.bind_apply
 
+#print Pmf.support_bind /-
 @[simp]
 theorem support_bind : (p.bind f).support = ⋃ a ∈ p.support, (f a).support :=
   Set.ext fun b => by simp [mem_support_iff, ENNReal.tsum_eq_zero, not_or]
 #align pmf.support_bind Pmf.support_bind
+-/
 
+/- warning: pmf.mem_support_bind_iff -> Pmf.mem_support_bind_iff is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} (p : Pmf.{u1} α) (f : α -> (Pmf.{u2} β)) (b : β), Iff (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) b (Pmf.support.{u2} β (Pmf.bind.{u1, u2} α β p f))) (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a (Pmf.support.{u1} α p)) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a (Pmf.support.{u1} α p)) => Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) b (Pmf.support.{u2} β (f a)))))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} (p : Pmf.{u1} α) (f : α -> (Pmf.{u2} β)) (b : β), Iff (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) b (Pmf.support.{u2} β (Pmf.bind.{u1, u2} α β p f))) (Exists.{succ u1} α (fun (a : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a (Pmf.support.{u1} α p)) (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) b (Pmf.support.{u2} β (f a)))))
+Case conversion may be inaccurate. Consider using '#align pmf.mem_support_bind_iff Pmf.mem_support_bind_iffₓ'. -/
 theorem mem_support_bind_iff (b : β) :
     b ∈ (p.bind f).support ↔ ∃ a ∈ p.support, b ∈ (f a).support := by
   simp only [support_bind, Set.mem_unionᵢ, Set.mem_setOf_eq]
 #align pmf.mem_support_bind_iff Pmf.mem_support_bind_iff
 
+#print Pmf.pure_bind /-
 @[simp]
 theorem pure_bind (a : α) (f : α → Pmf β) : (pure a).bind f = f a :=
   by
@@ -139,7 +192,9 @@ theorem pure_bind (a : α) (f : α → Pmf β) : (pure a).bind f = f a :=
     split_ifs <;> simp <;> subst h <;> simp
   ext b <;> simp [this]
 #align pmf.pure_bind Pmf.pure_bind
+-/
 
+#print Pmf.bind_pure /-
 @[simp]
 theorem bind_pure : p.bind pure = p :=
   Pmf.ext fun x =>
@@ -149,19 +204,34 @@ theorem bind_pure : p.bind pure = p :=
             rw [pure_apply_of_ne _ _ hy.symm, MulZeroClass.mul_zero]) <|
         by rw [pure_apply_self, mul_one])
 #align pmf.bind_pure Pmf.bind_pure
+-/
 
+/- warning: pmf.bind_const -> Pmf.bind_const is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} (p : Pmf.{u1} α) (q : Pmf.{u2} β), Eq.{succ u2} (Pmf.{u2} β) (Pmf.bind.{u1, u2} α β p (fun (_x : α) => q)) q
+but is expected to have type
+  forall {α : Type.{u2}} {β : Type.{u1}} (p : Pmf.{u2} α) (q : Pmf.{u1} β), Eq.{succ u1} (Pmf.{u1} β) (Pmf.bind.{u2, u1} α β p (fun (_x : α) => q)) q
+Case conversion may be inaccurate. Consider using '#align pmf.bind_const Pmf.bind_constₓ'. -/
 @[simp]
 theorem bind_const (p : Pmf α) (q : Pmf β) : (p.bind fun _ => q) = q :=
   Pmf.ext fun x => by rw [bind_apply, ENNReal.tsum_mul_right, tsum_coe, one_mul]
 #align pmf.bind_const Pmf.bind_const
 
+#print Pmf.bind_bind /-
 @[simp]
 theorem bind_bind : (p.bind f).bind g = p.bind fun a => (f a).bind g :=
   Pmf.ext fun b => by
     simpa only [ennreal.coe_eq_coe.symm, bind_apply, ennreal.tsum_mul_left.symm,
       ennreal.tsum_mul_right.symm, mul_assoc, mul_left_comm, mul_comm] using ENNReal.tsum_comm
 #align pmf.bind_bind Pmf.bind_bind
+-/
 
+/- warning: pmf.bind_comm -> Pmf.bind_comm is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} (p : Pmf.{u1} α) (q : Pmf.{u2} β) (f : α -> β -> (Pmf.{u3} γ)), Eq.{succ u3} (Pmf.{u3} γ) (Pmf.bind.{u1, u3} α γ p (fun (a : α) => Pmf.bind.{u2, u3} β γ q (f a))) (Pmf.bind.{u2, u3} β γ q (fun (b : β) => Pmf.bind.{u1, u3} α γ p (fun (a : α) => f a b)))
+but is expected to have type
+  forall {α : Type.{u3}} {β : Type.{u2}} {γ : Type.{u1}} (p : Pmf.{u3} α) (q : Pmf.{u2} β) (f : α -> β -> (Pmf.{u1} γ)), Eq.{succ u1} (Pmf.{u1} γ) (Pmf.bind.{u3, u1} α γ p (fun (a : α) => Pmf.bind.{u2, u1} β γ q (f a))) (Pmf.bind.{u2, u1} β γ q (fun (b : β) => Pmf.bind.{u3, u1} α γ p (fun (a : α) => f a b)))
+Case conversion may be inaccurate. Consider using '#align pmf.bind_comm Pmf.bind_commₓ'. -/
 theorem bind_comm (p : Pmf α) (q : Pmf β) (f : α → β → Pmf γ) :
     (p.bind fun a => q.bind (f a)) = q.bind fun b => p.bind fun a => f a b :=
   Pmf.ext fun b => by
@@ -173,6 +243,12 @@ section Measure
 
 variable (s : Set β)
 
+/- warning: pmf.to_outer_measure_bind_apply -> Pmf.toOuterMeasure_bind_apply is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} (p : Pmf.{u1} α) (f : α -> (Pmf.{u2} β)) (s : Set.{u2} β), Eq.{1} ENNReal (coeFn.{succ u2, succ u2} (MeasureTheory.OuterMeasure.{u2} β) (fun (_x : MeasureTheory.OuterMeasure.{u2} β) => (Set.{u2} β) -> ENNReal) (MeasureTheory.OuterMeasure.instCoeFun.{u2} β) (Pmf.toOuterMeasure.{u2} β (Pmf.bind.{u1, u2} α β p f)) s) (tsum.{0, u1} ENNReal (OrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))) ENNReal.topologicalSpace α (fun (a : α) => HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (Distrib.toHasMul.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (coeFn.{succ u1, succ u1} (Pmf.{u1} α) (fun (_x : Pmf.{u1} α) => α -> ENNReal) (FunLike.hasCoeToFun.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (p : α) => ENNReal) (Pmf.funLike.{u1} α)) p a) (coeFn.{succ u2, succ u2} (MeasureTheory.OuterMeasure.{u2} β) (fun (_x : MeasureTheory.OuterMeasure.{u2} β) => (Set.{u2} β) -> ENNReal) (MeasureTheory.OuterMeasure.instCoeFun.{u2} β) (Pmf.toOuterMeasure.{u2} β (f a)) s)))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} (p : Pmf.{u1} α) (f : α -> (Pmf.{u2} β)) (s : Set.{u2} β), Eq.{1} ENNReal (MeasureTheory.OuterMeasure.measureOf.{u2} β (Pmf.toOuterMeasure.{u2} β (Pmf.bind.{u1, u2} α β p f)) s) (tsum.{0, u1} ENNReal (LinearOrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (LinearOrderedAddCommMonoidWithTop.toLinearOrderedAddCommMonoid.{0} ENNReal ENNReal.instLinearOrderedAddCommMonoidWithTopENNReal)) ENNReal.instTopologicalSpaceENNReal α (fun (a : α) => HMul.hMul.{0, 0, 0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) ENNReal ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) (instHMul.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) (CanonicallyOrderedCommSemiring.toMul.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) ENNReal.instCanonicallyOrderedCommSemiringENNReal)) (FunLike.coe.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (_x : α) => (fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) _x) (Pmf.funLike.{u1} α) p a) (MeasureTheory.OuterMeasure.measureOf.{u2} β (Pmf.toOuterMeasure.{u2} β (f a)) s)))
+Case conversion may be inaccurate. Consider using '#align pmf.to_outer_measure_bind_apply Pmf.toOuterMeasure_bind_applyₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (b a) -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (a b) -/
 @[simp]
@@ -192,6 +268,12 @@ theorem toOuterMeasure_bind_apply :
     
 #align pmf.to_outer_measure_bind_apply Pmf.toOuterMeasure_bind_apply
 
+/- warning: pmf.to_measure_bind_apply -> Pmf.toMeasure_bind_apply is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} (p : Pmf.{u1} α) (f : α -> (Pmf.{u2} β)) (s : Set.{u2} β) [_inst_1 : MeasurableSpace.{u2} β], (MeasurableSet.{u2} β _inst_1 s) -> (Eq.{1} ENNReal (coeFn.{succ u2, succ u2} (MeasureTheory.Measure.{u2} β _inst_1) (fun (_x : MeasureTheory.Measure.{u2} β _inst_1) => (Set.{u2} β) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u2} β _inst_1) (Pmf.toMeasure.{u2} β _inst_1 (Pmf.bind.{u1, u2} α β p f)) s) (tsum.{0, u1} ENNReal (OrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))) ENNReal.topologicalSpace α (fun (a : α) => HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (Distrib.toHasMul.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (coeFn.{succ u1, succ u1} (Pmf.{u1} α) (fun (_x : Pmf.{u1} α) => α -> ENNReal) (FunLike.hasCoeToFun.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (p : α) => ENNReal) (Pmf.funLike.{u1} α)) p a) (coeFn.{succ u2, succ u2} (MeasureTheory.Measure.{u2} β _inst_1) (fun (_x : MeasureTheory.Measure.{u2} β _inst_1) => (Set.{u2} β) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u2} β _inst_1) (Pmf.toMeasure.{u2} β _inst_1 (f a)) s))))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} (p : Pmf.{u1} α) (f : α -> (Pmf.{u2} β)) (s : Set.{u2} β) [_inst_1 : MeasurableSpace.{u2} β], (MeasurableSet.{u2} β _inst_1 s) -> (Eq.{1} ENNReal (MeasureTheory.OuterMeasure.measureOf.{u2} β (MeasureTheory.Measure.toOuterMeasure.{u2} β _inst_1 (Pmf.toMeasure.{u2} β _inst_1 (Pmf.bind.{u1, u2} α β p f))) s) (tsum.{0, u1} ENNReal (LinearOrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (LinearOrderedAddCommMonoidWithTop.toLinearOrderedAddCommMonoid.{0} ENNReal ENNReal.instLinearOrderedAddCommMonoidWithTopENNReal)) ENNReal.instTopologicalSpaceENNReal α (fun (a : α) => HMul.hMul.{0, 0, 0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) ENNReal ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) (instHMul.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) (CanonicallyOrderedCommSemiring.toMul.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) ENNReal.instCanonicallyOrderedCommSemiringENNReal)) (FunLike.coe.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (_x : α) => (fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) _x) (Pmf.funLike.{u1} α) p a) (MeasureTheory.OuterMeasure.measureOf.{u2} β (MeasureTheory.Measure.toOuterMeasure.{u2} β _inst_1 (Pmf.toMeasure.{u2} β _inst_1 (f a))) s))))
+Case conversion may be inaccurate. Consider using '#align pmf.to_measure_bind_apply Pmf.toMeasure_bind_applyₓ'. -/
 /-- The measure of a set under `p.bind f` is the sum over `a : α`
   of the probability of `a` under `p` times the measure of the set under `f a` -/
 @[simp]
@@ -213,6 +295,7 @@ instance : Monad Pmf where
 
 section BindOnSupport
 
+#print Pmf.bindOnSupport /-
 /-- Generalized version of `bind` allowing `f` to only be defined on the support of `p`.
   `p.bind f` is equivalent to `p.bind_on_support (λ a _, f a)`, see `bind_on_support_eq_bind` -/
 def bindOnSupport (p : Pmf α) (f : ∀ a ∈ p.support, Pmf β) : Pmf β :=
@@ -225,15 +308,23 @@ def bindOnSupport (p : Pmf α) (f : ∀ a ∈ p.support, Pmf β) : Pmf β :=
         · simp only [h, MulZeroClass.zero_mul]
         · rw [(f a h).tsum_coe, mul_one])⟩
 #align pmf.bind_on_support Pmf.bindOnSupport
+-/
 
 variable {p : Pmf α} (f : ∀ a ∈ p.support, Pmf β)
 
+/- warning: pmf.bind_on_support_apply -> Pmf.bindOnSupport_apply is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} {p : Pmf.{u1} α} (f : forall (a : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a (Pmf.support.{u1} α p)) -> (Pmf.{u2} β)) (b : β), Eq.{1} ENNReal (coeFn.{succ u2, succ u2} (Pmf.{u2} β) (fun (_x : Pmf.{u2} β) => β -> ENNReal) (FunLike.hasCoeToFun.{succ u2, succ u2, 1} (Pmf.{u2} β) β (fun (p : β) => ENNReal) (Pmf.funLike.{u2} β)) (Pmf.bindOnSupport.{u1, u2} α β p f) b) (tsum.{0, u1} ENNReal (OrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))) ENNReal.topologicalSpace α (fun (a : α) => HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (Distrib.toHasMul.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (coeFn.{succ u1, succ u1} (Pmf.{u1} α) (fun (_x : Pmf.{u1} α) => α -> ENNReal) (FunLike.hasCoeToFun.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (p : α) => ENNReal) (Pmf.funLike.{u1} α)) p a) (dite.{1} ENNReal (Eq.{1} ENNReal (coeFn.{succ u1, succ u1} (Pmf.{u1} α) (fun (_x : Pmf.{u1} α) => α -> ENNReal) (FunLike.hasCoeToFun.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (p : α) => ENNReal) (Pmf.funLike.{u1} α)) p a) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (Option.decidableEq.{0} NNReal (fun (a : NNReal) (b : NNReal) => Subtype.decidableEq.{0} Real (fun (x : Real) => LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) x) (fun (a : Real) (b : Real) => Real.decidableEq a b) a b) (coeFn.{succ u1, succ u1} (Pmf.{u1} α) (fun (_x : Pmf.{u1} α) => α -> ENNReal) (FunLike.hasCoeToFun.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (p : α) => ENNReal) (Pmf.funLike.{u1} α)) p a) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (fun (h : Eq.{1} ENNReal (coeFn.{succ u1, succ u1} (Pmf.{u1} α) (fun (_x : Pmf.{u1} α) => α -> ENNReal) (FunLike.hasCoeToFun.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (p : α) => ENNReal) (Pmf.funLike.{u1} α)) p a) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) => OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) (fun (h : Not (Eq.{1} ENNReal (coeFn.{succ u1, succ u1} (Pmf.{u1} α) (fun (_x : Pmf.{u1} α) => α -> ENNReal) (FunLike.hasCoeToFun.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (p : α) => ENNReal) (Pmf.funLike.{u1} α)) p a) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))))) => coeFn.{succ u2, succ u2} (Pmf.{u2} β) (fun (_x : Pmf.{u2} β) => β -> ENNReal) (FunLike.hasCoeToFun.{succ u2, succ u2, 1} (Pmf.{u2} β) β (fun (p : β) => ENNReal) (Pmf.funLike.{u2} β)) (f a h) b))))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} {p : Pmf.{u1} α} (f : forall (a : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a (Pmf.support.{u1} α p)) -> (Pmf.{u2} β)) (b : β), Eq.{1} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : β) => ENNReal) b) (FunLike.coe.{succ u2, succ u2, 1} (Pmf.{u2} β) β (fun (_x : β) => (fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : β) => ENNReal) _x) (Pmf.funLike.{u2} β) (Pmf.bindOnSupport.{u1, u2} α β p f) b) (tsum.{0, u1} ENNReal (LinearOrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (LinearOrderedAddCommMonoidWithTop.toLinearOrderedAddCommMonoid.{0} ENNReal ENNReal.instLinearOrderedAddCommMonoidWithTopENNReal)) ENNReal.instTopologicalSpaceENNReal α (fun (a : α) => HMul.hMul.{0, 0, 0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : β) => ENNReal) b) ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) (instHMul.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) (CanonicallyOrderedCommSemiring.toMul.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) ENNReal.instCanonicallyOrderedCommSemiringENNReal)) (FunLike.coe.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (_x : α) => (fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) _x) (Pmf.funLike.{u1} α) p a) (dite.{1} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : β) => ENNReal) b) (Eq.{1} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) (FunLike.coe.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (_x : α) => (fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) _x) (Pmf.funLike.{u1} α) p a) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) 0 (Zero.toOfNat0.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) instENNRealZero))) (instDecidableEq.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) (instLinearOrder.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) ENNReal.instCompleteLinearOrderENNReal))) (FunLike.coe.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (_x : α) => (fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) _x) (Pmf.funLike.{u1} α) p a) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) 0 (Zero.toOfNat0.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) instENNRealZero))) (fun (h : Eq.{1} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) (FunLike.coe.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (_x : α) => (fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) _x) (Pmf.funLike.{u1} α) p a) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) 0 (Zero.toOfNat0.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) instENNRealZero))) => OfNat.ofNat.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : β) => ENNReal) b) 0 (Zero.toOfNat0.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : β) => ENNReal) b) instENNRealZero)) (fun (h : Not (Eq.{1} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) (FunLike.coe.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (_x : α) => (fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) _x) (Pmf.funLike.{u1} α) p a) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) 0 (Zero.toOfNat0.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) instENNRealZero)))) => FunLike.coe.{succ u2, succ u2, 1} (Pmf.{u2} β) β (fun (_x : β) => (fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : β) => ENNReal) _x) (Pmf.funLike.{u2} β) (f a h) b))))
+Case conversion may be inaccurate. Consider using '#align pmf.bind_on_support_apply Pmf.bindOnSupport_applyₓ'. -/
 @[simp]
 theorem bindOnSupport_apply (b : β) :
     p.bindOnSupport f b = ∑' a, p a * if h : p a = 0 then 0 else f a h b :=
   rfl
 #align pmf.bind_on_support_apply Pmf.bindOnSupport_apply
 
+#print Pmf.support_bindOnSupport /-
 @[simp]
 theorem support_bindOnSupport :
     (p.bindOnSupport f).support = ⋃ (a : α) (h : a ∈ p.support), (f a h).support :=
@@ -249,12 +340,21 @@ theorem support_bindOnSupport :
       let ⟨a, ha, ha'⟩ := hb
       ⟨a, ⟨ha, by simpa [(mem_support_iff _ a).1 ha] using ha'⟩⟩⟩
 #align pmf.support_bind_on_support Pmf.support_bindOnSupport
+-/
 
+#print Pmf.mem_support_bindOnSupport_iff /-
 theorem mem_support_bindOnSupport_iff (b : β) :
     b ∈ (p.bindOnSupport f).support ↔ ∃ (a : α)(h : a ∈ p.support), b ∈ (f a h).support := by
   simp only [support_bind_on_support, Set.mem_setOf_eq, Set.mem_unionᵢ]
 #align pmf.mem_support_bind_on_support_iff Pmf.mem_support_bindOnSupport_iff
+-/
 
+/- warning: pmf.bind_on_support_eq_bind -> Pmf.bindOnSupport_eq_bind is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} (p : Pmf.{u1} α) (f : α -> (Pmf.{u2} β)), Eq.{succ u2} (Pmf.{u2} β) (Pmf.bindOnSupport.{u1, u2} α β p (fun (a : α) (_x : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a (Pmf.support.{u1} α p)) => f a)) (Pmf.bind.{u1, u2} α β p f)
+but is expected to have type
+  forall {α : Type.{u2}} {β : Type.{u1}} (p : Pmf.{u2} α) (f : α -> (Pmf.{u1} β)), Eq.{succ u1} (Pmf.{u1} β) (Pmf.bindOnSupport.{u2, u1} α β p (fun (a : α) (_x : Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) a (Pmf.support.{u2} α p)) => f a)) (Pmf.bind.{u2, u1} α β p f)
+Case conversion may be inaccurate. Consider using '#align pmf.bind_on_support_eq_bind Pmf.bindOnSupport_eq_bindₓ'. -/
 /-- `bind_on_support` reduces to `bind` if `f` doesn't depend on the additional hypothesis -/
 @[simp]
 theorem bindOnSupport_eq_bind (p : Pmf α) (f : α → Pmf β) :
@@ -267,6 +367,12 @@ theorem bindOnSupport_eq_bind (p : Pmf α) (f : α → Pmf β) :
     MulZeroClass.mul_zero, this]
 #align pmf.bind_on_support_eq_bind Pmf.bindOnSupport_eq_bind
 
+/- warning: pmf.bind_on_support_eq_zero_iff -> Pmf.bindOnSupport_eq_zero_iff is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} {p : Pmf.{u1} α} (f : forall (a : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a (Pmf.support.{u1} α p)) -> (Pmf.{u2} β)) (b : β), Iff (Eq.{1} ENNReal (coeFn.{succ u2, succ u2} (Pmf.{u2} β) (fun (_x : Pmf.{u2} β) => β -> ENNReal) (FunLike.hasCoeToFun.{succ u2, succ u2, 1} (Pmf.{u2} β) β (fun (p : β) => ENNReal) (Pmf.funLike.{u2} β)) (Pmf.bindOnSupport.{u1, u2} α β p f) b) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (forall (a : α) (ha : Ne.{1} ENNReal (coeFn.{succ u1, succ u1} (Pmf.{u1} α) (fun (_x : Pmf.{u1} α) => α -> ENNReal) (FunLike.hasCoeToFun.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (p : α) => ENNReal) (Pmf.funLike.{u1} α)) p a) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))), Eq.{1} ENNReal (coeFn.{succ u2, succ u2} (Pmf.{u2} β) (fun (_x : Pmf.{u2} β) => β -> ENNReal) (FunLike.hasCoeToFun.{succ u2, succ u2, 1} (Pmf.{u2} β) β (fun (p : β) => ENNReal) (Pmf.funLike.{u2} β)) (f a ha) b) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} {p : Pmf.{u1} α} (f : forall (a : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a (Pmf.support.{u1} α p)) -> (Pmf.{u2} β)) (b : β), Iff (Eq.{1} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : β) => ENNReal) b) (FunLike.coe.{succ u2, succ u2, 1} (Pmf.{u2} β) β (fun (_x : β) => (fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : β) => ENNReal) _x) (Pmf.funLike.{u2} β) (Pmf.bindOnSupport.{u1, u2} α β p f) b) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : β) => ENNReal) b) 0 (Zero.toOfNat0.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : β) => ENNReal) b) instENNRealZero))) (forall (a : α) (ha : Ne.{1} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) (FunLike.coe.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (_x : α) => (fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) _x) (Pmf.funLike.{u1} α) p a) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) 0 (Zero.toOfNat0.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) instENNRealZero))), Eq.{1} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : β) => ENNReal) b) (FunLike.coe.{succ u2, succ u2, 1} (Pmf.{u2} β) β (fun (_x : β) => (fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : β) => ENNReal) _x) (Pmf.funLike.{u2} β) (f a ha) b) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : β) => ENNReal) b) 0 (Zero.toOfNat0.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : β) => ENNReal) b) instENNRealZero)))
+Case conversion may be inaccurate. Consider using '#align pmf.bind_on_support_eq_zero_iff Pmf.bindOnSupport_eq_zero_iffₓ'. -/
 theorem bindOnSupport_eq_zero_iff (b : β) :
     p.bindOnSupport f b = 0 ↔ ∀ (a) (ha : p a ≠ 0), f a ha b = 0 :=
   by
@@ -274,6 +380,12 @@ theorem bindOnSupport_eq_zero_iff (b : β) :
   exact ⟨fun h a ha => trans (dif_neg ha).symm (h a ha), fun h a ha => trans (dif_neg ha) (h a ha)⟩
 #align pmf.bind_on_support_eq_zero_iff Pmf.bindOnSupport_eq_zero_iff
 
+/- warning: pmf.pure_bind_on_support -> Pmf.pure_bindOnSupport is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} (a : α) (f : forall (a' : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a' (Pmf.support.{u1} α (Pmf.pure.{u1} α a))) -> (Pmf.{u2} β)), Eq.{succ u2} (Pmf.{u2} β) (Pmf.bindOnSupport.{u1, u2} α β (Pmf.pure.{u1} α a) f) (f a (Iff.mpr (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a (Pmf.support.{u1} α (Pmf.pure.{u1} α a))) (Eq.{succ u1} α a a) (Pmf.mem_support_pure_iff.{u1} α a a) (rfl.{succ u1} α a)))
+but is expected to have type
+  forall {α : Type.{u2}} {β : Type.{u1}} (a : α) (f : forall (a' : α), (Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) a' (Pmf.support.{u2} α (Pmf.pure.{u2} α a))) -> (Pmf.{u1} β)), Eq.{succ u1} (Pmf.{u1} β) (Pmf.bindOnSupport.{u2, u1} α β (Pmf.pure.{u2} α a) f) (f a (Iff.mpr (Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) a (Pmf.support.{u2} α (Pmf.pure.{u2} α a))) (Eq.{succ u2} α a a) (Pmf.mem_support_pure_iff.{u2} α a a) (rfl.{succ u2} α a)))
+Case conversion may be inaccurate. Consider using '#align pmf.pure_bind_on_support Pmf.pure_bindOnSupportₓ'. -/
 @[simp]
 theorem pure_bindOnSupport (a : α) (f : ∀ (a' : α) (ha : a' ∈ (pure a).support), Pmf β) :
     (pure a).bindOnSupport f = f a ((mem_support_pure_iff a a).mpr rfl) :=
@@ -284,10 +396,18 @@ theorem pure_bindOnSupport (a : α) (f : ∀ (a' : α) (ha : a' ∈ (pure a).sup
   by_cases h : a' = a <;> simp [h]
 #align pmf.pure_bind_on_support Pmf.pure_bindOnSupport
 
+#print Pmf.bindOnSupport_pure /-
 theorem bindOnSupport_pure (p : Pmf α) : (p.bindOnSupport fun a _ => pure a) = p := by
   simp only [Pmf.bind_pure, Pmf.bindOnSupport_eq_bind]
 #align pmf.bind_on_support_pure Pmf.bindOnSupport_pure
+-/
 
+/- warning: pmf.bind_on_support_bind_on_support -> Pmf.bindOnSupport_bindOnSupport is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} (p : Pmf.{u1} α) (f : forall (a : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a (Pmf.support.{u1} α p)) -> (Pmf.{u2} β)) (g : forall (b : β), (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) b (Pmf.support.{u2} β (Pmf.bindOnSupport.{u1, u2} α β p f))) -> (Pmf.{u3} γ)), Eq.{succ u3} (Pmf.{u3} γ) (Pmf.bindOnSupport.{u2, u3} β γ (Pmf.bindOnSupport.{u1, u2} α β p f) g) (Pmf.bindOnSupport.{u1, u3} α γ p (fun (a : α) (ha : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a (Pmf.support.{u1} α p)) => Pmf.bindOnSupport.{u2, u3} β γ (f a ha) (fun (b : β) (hb : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) b (Pmf.support.{u2} β (f a ha))) => g b (Iff.mpr (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) b (Pmf.support.{u2} β (Pmf.bindOnSupport.{u1, u2} α β p f))) (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a (Pmf.support.{u1} α p)) (fun (h : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a (Pmf.support.{u1} α p)) => Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) b (Pmf.support.{u2} β (f a h))))) (Pmf.mem_support_bindOnSupport_iff.{u1, u2} α β p f b) (Exists.intro.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a (Pmf.support.{u1} α p)) (fun (h : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a (Pmf.support.{u1} α p)) => Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) b (Pmf.support.{u2} β (f a h)))) a (Exists.intro.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a (Pmf.support.{u1} α p)) (fun (h : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a (Pmf.support.{u1} α p)) => Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) b (Pmf.support.{u2} β (f a h))) ha hb))))))
+but is expected to have type
+  forall {α : Type.{u3}} {β : Type.{u2}} {γ : Type.{u1}} (p : Pmf.{u3} α) (f : forall (a : α), (Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) a (Pmf.support.{u3} α p)) -> (Pmf.{u2} β)) (g : forall (b : β), (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) b (Pmf.support.{u2} β (Pmf.bindOnSupport.{u3, u2} α β p f))) -> (Pmf.{u1} γ)), Eq.{succ u1} (Pmf.{u1} γ) (Pmf.bindOnSupport.{u2, u1} β γ (Pmf.bindOnSupport.{u3, u2} α β p f) g) (Pmf.bindOnSupport.{u3, u1} α γ p (fun (a : α) (ha : Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) a (Pmf.support.{u3} α p)) => Pmf.bindOnSupport.{u2, u1} β γ (f a ha) (fun (b : β) (hb : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) b (Pmf.support.{u2} β (f a ha))) => g b (Iff.mpr (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) b (Pmf.support.{u2} β (Pmf.bindOnSupport.{u3, u2} α β p f))) (Exists.{succ u3} α (fun (a : α) => Exists.{0} (Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) a (Pmf.support.{u3} α p)) (fun (h : Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) a (Pmf.support.{u3} α p)) => Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) b (Pmf.support.{u2} β (f a h))))) (Pmf.mem_support_bindOnSupport_iff.{u3, u2} α β p f b) (Exists.intro.{succ u3} α (fun (a : α) => Exists.{0} (Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) a (Pmf.support.{u3} α p)) (fun (h : Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) a (Pmf.support.{u3} α p)) => Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) b (Pmf.support.{u2} β (f a h)))) a (Exists.intro.{0} (Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) a (Pmf.support.{u3} α p)) (fun (h : Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) a (Pmf.support.{u3} α p)) => Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) b (Pmf.support.{u2} β (f a h))) ha hb))))))
+Case conversion may be inaccurate. Consider using '#align pmf.bind_on_support_bind_on_support Pmf.bindOnSupport_bindOnSupportₓ'. -/
 @[simp]
 theorem bindOnSupport_bindOnSupport (p : Pmf α) (f : ∀ a ∈ p.support, Pmf β)
     (g : ∀ b ∈ (p.bindOnSupport f).support, Pmf γ) :
@@ -310,6 +430,12 @@ theorem bindOnSupport_bindOnSupport (p : Pmf α) (f : ∀ a ∈ p.support, Pmf 
   · simp [h_2]
 #align pmf.bind_on_support_bind_on_support Pmf.bindOnSupport_bindOnSupport
 
+/- warning: pmf.bind_on_support_comm -> Pmf.bindOnSupport_comm is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} (p : Pmf.{u1} α) (q : Pmf.{u2} β) (f : forall (a : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a (Pmf.support.{u1} α p)) -> (forall (b : β), (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) b (Pmf.support.{u2} β q)) -> (Pmf.{u3} γ))), Eq.{succ u3} (Pmf.{u3} γ) (Pmf.bindOnSupport.{u1, u3} α γ p (fun (a : α) (ha : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a (Pmf.support.{u1} α p)) => Pmf.bindOnSupport.{u2, u3} β γ q (f a ha))) (Pmf.bindOnSupport.{u2, u3} β γ q (fun (b : β) (hb : Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) b (Pmf.support.{u2} β q)) => Pmf.bindOnSupport.{u1, u3} α γ p (fun (a : α) (ha : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a (Pmf.support.{u1} α p)) => f a ha b hb)))
+but is expected to have type
+  forall {α : Type.{u3}} {β : Type.{u2}} {γ : Type.{u1}} (p : Pmf.{u3} α) (q : Pmf.{u2} β) (f : forall (a : α), (Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) a (Pmf.support.{u3} α p)) -> (forall (b : β), (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) b (Pmf.support.{u2} β q)) -> (Pmf.{u1} γ))), Eq.{succ u1} (Pmf.{u1} γ) (Pmf.bindOnSupport.{u3, u1} α γ p (fun (a : α) (ha : Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) a (Pmf.support.{u3} α p)) => Pmf.bindOnSupport.{u2, u1} β γ q (f a ha))) (Pmf.bindOnSupport.{u2, u1} β γ q (fun (b : β) (hb : Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) b (Pmf.support.{u2} β q)) => Pmf.bindOnSupport.{u3, u1} α γ p (fun (a : α) (ha : Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) a (Pmf.support.{u3} α p)) => f a ha b hb)))
+Case conversion may be inaccurate. Consider using '#align pmf.bind_on_support_comm Pmf.bindOnSupport_commₓ'. -/
 theorem bindOnSupport_comm (p : Pmf α) (q : Pmf β) (f : ∀ a ∈ p.support, ∀ b ∈ q.support, Pmf γ) :
     (p.bindOnSupport fun a ha => q.bindOnSupport (f a ha)) =
       q.bindOnSupport fun b hb => p.bindOnSupport fun a ha => f a ha b hb :=
@@ -325,6 +451,12 @@ section Measure
 
 variable (s : Set β)
 
+/- warning: pmf.to_outer_measure_bind_on_support_apply -> Pmf.toOuterMeasure_bindOnSupport_apply is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} {p : Pmf.{u1} α} (f : forall (a : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a (Pmf.support.{u1} α p)) -> (Pmf.{u2} β)) (s : Set.{u2} β), Eq.{1} ENNReal (coeFn.{succ u2, succ u2} (MeasureTheory.OuterMeasure.{u2} β) (fun (_x : MeasureTheory.OuterMeasure.{u2} β) => (Set.{u2} β) -> ENNReal) (MeasureTheory.OuterMeasure.instCoeFun.{u2} β) (Pmf.toOuterMeasure.{u2} β (Pmf.bindOnSupport.{u1, u2} α β p f)) s) (tsum.{0, u1} ENNReal (OrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))) ENNReal.topologicalSpace α (fun (a : α) => HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (Distrib.toHasMul.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (coeFn.{succ u1, succ u1} (Pmf.{u1} α) (fun (_x : Pmf.{u1} α) => α -> ENNReal) (FunLike.hasCoeToFun.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (p : α) => ENNReal) (Pmf.funLike.{u1} α)) p a) (dite.{1} ENNReal (Eq.{1} ENNReal (coeFn.{succ u1, succ u1} (Pmf.{u1} α) (fun (_x : Pmf.{u1} α) => α -> ENNReal) (FunLike.hasCoeToFun.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (p : α) => ENNReal) (Pmf.funLike.{u1} α)) p a) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (Option.decidableEq.{0} NNReal (fun (a : NNReal) (b : NNReal) => Subtype.decidableEq.{0} Real (fun (x : Real) => LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) x) (fun (a : Real) (b : Real) => Real.decidableEq a b) a b) (coeFn.{succ u1, succ u1} (Pmf.{u1} α) (fun (_x : Pmf.{u1} α) => α -> ENNReal) (FunLike.hasCoeToFun.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (p : α) => ENNReal) (Pmf.funLike.{u1} α)) p a) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (fun (h : Eq.{1} ENNReal (coeFn.{succ u1, succ u1} (Pmf.{u1} α) (fun (_x : Pmf.{u1} α) => α -> ENNReal) (FunLike.hasCoeToFun.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (p : α) => ENNReal) (Pmf.funLike.{u1} α)) p a) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) => OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) (fun (h : Not (Eq.{1} ENNReal (coeFn.{succ u1, succ u1} (Pmf.{u1} α) (fun (_x : Pmf.{u1} α) => α -> ENNReal) (FunLike.hasCoeToFun.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (p : α) => ENNReal) (Pmf.funLike.{u1} α)) p a) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))))) => coeFn.{succ u2, succ u2} (MeasureTheory.OuterMeasure.{u2} β) (fun (_x : MeasureTheory.OuterMeasure.{u2} β) => (Set.{u2} β) -> ENNReal) (MeasureTheory.OuterMeasure.instCoeFun.{u2} β) (Pmf.toOuterMeasure.{u2} β (f a h)) s))))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} {p : Pmf.{u1} α} (f : forall (a : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a (Pmf.support.{u1} α p)) -> (Pmf.{u2} β)) (s : Set.{u2} β), Eq.{1} ENNReal (MeasureTheory.OuterMeasure.measureOf.{u2} β (Pmf.toOuterMeasure.{u2} β (Pmf.bindOnSupport.{u1, u2} α β p f)) s) (tsum.{0, u1} ENNReal (LinearOrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (LinearOrderedAddCommMonoidWithTop.toLinearOrderedAddCommMonoid.{0} ENNReal ENNReal.instLinearOrderedAddCommMonoidWithTopENNReal)) ENNReal.instTopologicalSpaceENNReal α (fun (a : α) => HMul.hMul.{0, 0, 0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) ENNReal ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) (instHMul.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) (CanonicallyOrderedCommSemiring.toMul.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) ENNReal.instCanonicallyOrderedCommSemiringENNReal)) (FunLike.coe.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (_x : α) => (fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) _x) (Pmf.funLike.{u1} α) p a) (dite.{1} ENNReal (Eq.{1} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) (FunLike.coe.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (_x : α) => (fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) _x) (Pmf.funLike.{u1} α) p a) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) 0 (Zero.toOfNat0.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) instENNRealZero))) (instDecidableEq.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) (instLinearOrder.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) ENNReal.instCompleteLinearOrderENNReal))) (FunLike.coe.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (_x : α) => (fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) _x) (Pmf.funLike.{u1} α) p a) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) 0 (Zero.toOfNat0.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) instENNRealZero))) (fun (h : Eq.{1} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) (FunLike.coe.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (_x : α) => (fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) _x) (Pmf.funLike.{u1} α) p a) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) 0 (Zero.toOfNat0.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) instENNRealZero))) => OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) (fun (h : Not (Eq.{1} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) (FunLike.coe.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (_x : α) => (fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) _x) (Pmf.funLike.{u1} α) p a) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) 0 (Zero.toOfNat0.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) instENNRealZero)))) => MeasureTheory.OuterMeasure.measureOf.{u2} β (Pmf.toOuterMeasure.{u2} β (f a h)) s))))
+Case conversion may be inaccurate. Consider using '#align pmf.to_outer_measure_bind_on_support_apply Pmf.toOuterMeasure_bindOnSupport_applyₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (a b) -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (b a) -/
 @[simp]
@@ -346,6 +478,12 @@ theorem toOuterMeasure_bindOnSupport_apply :
     
 #align pmf.to_outer_measure_bind_on_support_apply Pmf.toOuterMeasure_bindOnSupport_apply
 
+/- warning: pmf.to_measure_bind_on_support_apply -> Pmf.toMeasure_bindOnSupport_apply is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} {p : Pmf.{u1} α} (f : forall (a : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a (Pmf.support.{u1} α p)) -> (Pmf.{u2} β)) (s : Set.{u2} β) [_inst_1 : MeasurableSpace.{u2} β], (MeasurableSet.{u2} β _inst_1 s) -> (Eq.{1} ENNReal (coeFn.{succ u2, succ u2} (MeasureTheory.Measure.{u2} β _inst_1) (fun (_x : MeasureTheory.Measure.{u2} β _inst_1) => (Set.{u2} β) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u2} β _inst_1) (Pmf.toMeasure.{u2} β _inst_1 (Pmf.bindOnSupport.{u1, u2} α β p f)) s) (tsum.{0, u1} ENNReal (OrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))) ENNReal.topologicalSpace α (fun (a : α) => HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (Distrib.toHasMul.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (coeFn.{succ u1, succ u1} (Pmf.{u1} α) (fun (_x : Pmf.{u1} α) => α -> ENNReal) (FunLike.hasCoeToFun.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (p : α) => ENNReal) (Pmf.funLike.{u1} α)) p a) (dite.{1} ENNReal (Eq.{1} ENNReal (coeFn.{succ u1, succ u1} (Pmf.{u1} α) (fun (_x : Pmf.{u1} α) => α -> ENNReal) (FunLike.hasCoeToFun.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (p : α) => ENNReal) (Pmf.funLike.{u1} α)) p a) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (Option.decidableEq.{0} NNReal (fun (a : NNReal) (b : NNReal) => Subtype.decidableEq.{0} Real (fun (x : Real) => LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) x) (fun (a : Real) (b : Real) => Real.decidableEq a b) a b) (coeFn.{succ u1, succ u1} (Pmf.{u1} α) (fun (_x : Pmf.{u1} α) => α -> ENNReal) (FunLike.hasCoeToFun.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (p : α) => ENNReal) (Pmf.funLike.{u1} α)) p a) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (fun (h : Eq.{1} ENNReal (coeFn.{succ u1, succ u1} (Pmf.{u1} α) (fun (_x : Pmf.{u1} α) => α -> ENNReal) (FunLike.hasCoeToFun.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (p : α) => ENNReal) (Pmf.funLike.{u1} α)) p a) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) => OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) (fun (h : Not (Eq.{1} ENNReal (coeFn.{succ u1, succ u1} (Pmf.{u1} α) (fun (_x : Pmf.{u1} α) => α -> ENNReal) (FunLike.hasCoeToFun.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (p : α) => ENNReal) (Pmf.funLike.{u1} α)) p a) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))))) => coeFn.{succ u2, succ u2} (MeasureTheory.Measure.{u2} β _inst_1) (fun (_x : MeasureTheory.Measure.{u2} β _inst_1) => (Set.{u2} β) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u2} β _inst_1) (Pmf.toMeasure.{u2} β _inst_1 (f a h)) s)))))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} {p : Pmf.{u1} α} (f : forall (a : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a (Pmf.support.{u1} α p)) -> (Pmf.{u2} β)) (s : Set.{u2} β) [_inst_1 : MeasurableSpace.{u2} β], (MeasurableSet.{u2} β _inst_1 s) -> (Eq.{1} ENNReal (MeasureTheory.OuterMeasure.measureOf.{u2} β (MeasureTheory.Measure.toOuterMeasure.{u2} β _inst_1 (Pmf.toMeasure.{u2} β _inst_1 (Pmf.bindOnSupport.{u1, u2} α β p f))) s) (tsum.{0, u1} ENNReal (LinearOrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (LinearOrderedAddCommMonoidWithTop.toLinearOrderedAddCommMonoid.{0} ENNReal ENNReal.instLinearOrderedAddCommMonoidWithTopENNReal)) ENNReal.instTopologicalSpaceENNReal α (fun (a : α) => HMul.hMul.{0, 0, 0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) ENNReal ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) (instHMul.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) (CanonicallyOrderedCommSemiring.toMul.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) ENNReal.instCanonicallyOrderedCommSemiringENNReal)) (FunLike.coe.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (_x : α) => (fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) _x) (Pmf.funLike.{u1} α) p a) (dite.{1} ENNReal (Eq.{1} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) (FunLike.coe.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (_x : α) => (fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) _x) (Pmf.funLike.{u1} α) p a) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) 0 (Zero.toOfNat0.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) instENNRealZero))) (instDecidableEq.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) (instLinearOrder.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) ENNReal.instCompleteLinearOrderENNReal))) (FunLike.coe.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (_x : α) => (fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) _x) (Pmf.funLike.{u1} α) p a) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) 0 (Zero.toOfNat0.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) instENNRealZero))) (fun (h : Eq.{1} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) (FunLike.coe.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (_x : α) => (fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) _x) (Pmf.funLike.{u1} α) p a) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) 0 (Zero.toOfNat0.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) instENNRealZero))) => OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) (fun (h : Not (Eq.{1} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) (FunLike.coe.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (_x : α) => (fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) _x) (Pmf.funLike.{u1} α) p a) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) 0 (Zero.toOfNat0.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) instENNRealZero)))) => MeasureTheory.OuterMeasure.measureOf.{u2} β (MeasureTheory.Measure.toOuterMeasure.{u2} β _inst_1 (Pmf.toMeasure.{u2} β _inst_1 (f a h))) s)))))
+Case conversion may be inaccurate. Consider using '#align pmf.to_measure_bind_on_support_apply Pmf.toMeasure_bindOnSupport_applyₓ'. -/
 /-- The measure of a set under `p.bind_on_support f` is the sum over `a : α`
   of the probability of `a` under `p` times the measure of the set under `f a _`.
   The additional if statement is needed since `f` is only a partial function -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/3180fab693e2cee3bff62675571264cb8778b212

@@ -144,8 +144,10 @@ theorem pure_bind (a : α) (f : α → Pmf β) : (pure a).bind f = f a :=
 theorem bind_pure : p.bind pure = p :=
   Pmf.ext fun x =>
     (bind_apply _ _ _).trans
-      (trans (tsum_eq_single x fun y hy => by rw [pure_apply_of_ne _ _ hy.symm, mul_zero]) <| by
-        rw [pure_apply_self, mul_one])
+      (trans
+          (tsum_eq_single x fun y hy => by
+            rw [pure_apply_of_ne _ _ hy.symm, MulZeroClass.mul_zero]) <|
+        by rw [pure_apply_self, mul_one])
 #align pmf.bind_pure Pmf.bind_pure
 
 @[simp]
@@ -220,7 +222,7 @@ def bindOnSupport (p : Pmf α) (f : ∀ a ∈ p.support, Pmf β) : Pmf β :=
         refine' ennreal.tsum_comm.trans (trans (tsum_congr fun a => _) p.tsum_coe)
         simp_rw [ENNReal.tsum_mul_left]
         split_ifs with h
-        · simp only [h, zero_mul]
+        · simp only [h, MulZeroClass.zero_mul]
         · rw [(f a h).tsum_coe, mul_one])⟩
 #align pmf.bind_on_support Pmf.bindOnSupport
 
@@ -260,9 +262,9 @@ theorem bindOnSupport_eq_bind (p : Pmf α) (f : α → Pmf β) :
   by
   ext (b x)
   have : ∀ a, ite (p a = 0) 0 (p a * f a b) = p a * f a b := fun a =>
-    ite_eq_right_iff.2 fun h => h.symm ▸ symm (zero_mul <| f a b)
-  simp only [bind_on_support_apply fun a _ => f a, p.bind_apply f, dite_eq_ite, mul_ite, mul_zero,
-    this]
+    ite_eq_right_iff.2 fun h => h.symm ▸ symm (MulZeroClass.zero_mul <| f a b)
+  simp only [bind_on_support_apply fun a _ => f a, p.bind_apply f, dite_eq_ite, mul_ite,
+    MulZeroClass.mul_zero, this]
 #align pmf.bind_on_support_eq_bind Pmf.bindOnSupport_eq_bind
 
 theorem bindOnSupport_eq_zero_iff (b : β) :
@@ -338,7 +340,7 @@ theorem toOuterMeasure_bindOnSupport_apply :
     _ = ∑' (a) (b), ite (b ∈ s) (p a * dite (p a = 0) (fun h => 0) fun h => f a h b) 0 :=
       ENNReal.tsum_comm
     _ = ∑' a, p a * ∑' b, ite (b ∈ s) (dite (p a = 0) (fun h => 0) fun h => f a h b) 0 :=
-      (tsum_congr fun a => by simp only [← ENNReal.tsum_mul_left, mul_ite, mul_zero])
+      (tsum_congr fun a => by simp only [← ENNReal.tsum_mul_left, mul_ite, MulZeroClass.mul_zero])
     _ = ∑' a, p a * dite (p a = 0) (fun h => 0) fun h => ∑' b, ite (b ∈ s) (f a h b) 0 :=
       tsum_congr fun a => by split_ifs with ha <;> simp only [if_t_t, tsum_zero, eq_self_iff_true]
     

mathlib commit https://github.com/leanprover-community/mathlib/commit/3180fab693e2cee3bff62675571264cb8778b212

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Devon Tuma
 
 ! This file was ported from Lean 3 source module probability.probability_mass_function.monad
-! leanprover-community/mathlib commit 3f5c9d30716c775bda043456728a1a3ee31412e7
+! leanprover-community/mathlib commit 4ac69b290818724c159de091daa3acd31da0ee6d
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -57,6 +57,15 @@ theorem support_pure : (pure a).support = {a} :=
 theorem mem_support_pure_iff : a' ∈ (pure a).support ↔ a' = a := by simp
 #align pmf.mem_support_pure_iff Pmf.mem_support_pure_iff
 
+@[simp]
+theorem pure_apply_self : pure a a = 1 :=
+  if_pos rfl
+#align pmf.pure_apply_self Pmf.pure_apply_self
+
+theorem pure_apply_of_ne (h : a' ≠ a) : pure a a' = 0 :=
+  if_neg h
+#align pmf.pure_apply_of_ne Pmf.pure_apply_of_ne
+
 instance [Inhabited α] : Inhabited (Pmf α) :=
   ⟨pure default⟩
 
@@ -133,12 +142,17 @@ theorem pure_bind (a : α) (f : α → Pmf β) : (pure a).bind f = f a :=
 
 @[simp]
 theorem bind_pure : p.bind pure = p :=
-  by
-  have : ∀ a a', p a * ite (a' = a) 1 0 = ite (a = a') (p a') 0 := fun a a' => by
-    split_ifs <;> try subst a <;> try subst a' <;> simp_all
-  ext b <;> simp [this]
+  Pmf.ext fun x =>
+    (bind_apply _ _ _).trans
+      (trans (tsum_eq_single x fun y hy => by rw [pure_apply_of_ne _ _ hy.symm, mul_zero]) <| by
+        rw [pure_apply_self, mul_one])
 #align pmf.bind_pure Pmf.bind_pure
 
+@[simp]
+theorem bind_const (p : Pmf α) (q : Pmf β) : (p.bind fun _ => q) = q :=
+  Pmf.ext fun x => by rw [bind_apply, ENNReal.tsum_mul_right, tsum_coe, one_mul]
+#align pmf.bind_const Pmf.bind_const
+
 @[simp]
 theorem bind_bind : (p.bind f).bind g = p.bind fun a => (f a).bind g :=
   Pmf.ext fun b => by

mathlib commit https://github.com/leanprover-community/mathlib/commit/4c586d291f189eecb9d00581aeb3dd998ac34442

@@ -165,12 +165,12 @@ theorem toOuterMeasure_bind_apply :
   calc
     (p.bind f).toOuterMeasure s = ∑' b, if b ∈ s then ∑' a, p a * f a b else 0 := by
       simp [to_outer_measure_apply, Set.indicator_apply]
-    _ = ∑' (b) (a), p a * if b ∈ s then f a b else 0 := tsum_congr fun b => by split_ifs <;> simp
+    _ = ∑' (b) (a), p a * if b ∈ s then f a b else 0 := (tsum_congr fun b => by split_ifs <;> simp)
     _ = ∑' (a) (b), p a * if b ∈ s then f a b else 0 :=
-      tsum_comm' ENNReal.summable (fun _ => ENNReal.summable) fun _ => ENNReal.summable
-    _ = ∑' a, p a * ∑' b, if b ∈ s then f a b else 0 := tsum_congr fun a => ENNReal.tsum_mul_left
+      (tsum_comm' ENNReal.summable (fun _ => ENNReal.summable) fun _ => ENNReal.summable)
+    _ = ∑' a, p a * ∑' b, if b ∈ s then f a b else 0 := (tsum_congr fun a => ENNReal.tsum_mul_left)
     _ = ∑' a, p a * ∑' b, if b ∈ s then f a b else 0 :=
-      tsum_congr fun a => (congr_arg fun x => p a * x) <| tsum_congr fun b => by split_ifs <;> rfl
+      (tsum_congr fun a => (congr_arg fun x => p a * x) <| tsum_congr fun b => by split_ifs <;> rfl)
     _ = ∑' a, p a * (f a).toOuterMeasure s :=
       tsum_congr fun a => by simp only [to_outer_measure_apply, Set.indicator_apply]
     
@@ -309,8 +309,8 @@ section Measure
 
 variable (s : Set β)
 
-/- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (b a) -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (a b) -/
+/- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (b a) -/
 @[simp]
 theorem toOuterMeasure_bindOnSupport_apply :
     (p.bindOnSupport f).toOuterMeasure s =
@@ -324,7 +324,7 @@ theorem toOuterMeasure_bindOnSupport_apply :
     _ = ∑' (a) (b), ite (b ∈ s) (p a * dite (p a = 0) (fun h => 0) fun h => f a h b) 0 :=
       ENNReal.tsum_comm
     _ = ∑' a, p a * ∑' b, ite (b ∈ s) (dite (p a = 0) (fun h => 0) fun h => f a h b) 0 :=
-      tsum_congr fun a => by simp only [← ENNReal.tsum_mul_left, mul_ite, mul_zero]
+      (tsum_congr fun a => by simp only [← ENNReal.tsum_mul_left, mul_ite, mul_zero])
     _ = ∑' a, p a * dite (p a = 0) (fun h => 0) fun h => ∑' b, ite (b ∈ s) (f a h b) 0 :=
       tsum_congr fun a => by split_ifs with ha <;> simp only [if_t_t, tsum_zero, eq_self_iff_true]
     

mathlib commit https://github.com/leanprover-community/mathlib/commit/eb0cb4511aaef0da2462207b67358a0e1fe1e2ee

@@ -28,7 +28,7 @@ noncomputable section
 
 variable {α β γ : Type _}
 
-open Classical BigOperators NNReal Ennreal
+open Classical BigOperators NNReal ENNReal
 
 open MeasureTheory
 
@@ -102,8 +102,8 @@ section Bind
 /-- The monadic bind operation for `pmf`. -/
 def bind (p : Pmf α) (f : α → Pmf β) : Pmf β :=
   ⟨fun b => ∑' a, p a * f a b,
-    Ennreal.summable.hasSum_iff.2
-      (Ennreal.tsum_comm.trans <| by simp only [Ennreal.tsum_mul_left, tsum_coe, mul_one])⟩
+    ENNReal.summable.hasSum_iff.2
+      (ENNReal.tsum_comm.trans <| by simp only [ENNReal.tsum_mul_left, tsum_coe, mul_one])⟩
 #align pmf.bind Pmf.bind
 
 variable (p : Pmf α) (f : α → Pmf β) (g : β → Pmf γ)
@@ -115,7 +115,7 @@ theorem bind_apply (b : β) : p.bind f b = ∑' a, p a * f a b :=
 
 @[simp]
 theorem support_bind : (p.bind f).support = ⋃ a ∈ p.support, (f a).support :=
-  Set.ext fun b => by simp [mem_support_iff, Ennreal.tsum_eq_zero, not_or]
+  Set.ext fun b => by simp [mem_support_iff, ENNReal.tsum_eq_zero, not_or]
 #align pmf.support_bind Pmf.support_bind
 
 theorem mem_support_bind_iff (b : β) :
@@ -143,14 +143,14 @@ theorem bind_pure : p.bind pure = p :=
 theorem bind_bind : (p.bind f).bind g = p.bind fun a => (f a).bind g :=
   Pmf.ext fun b => by
     simpa only [ennreal.coe_eq_coe.symm, bind_apply, ennreal.tsum_mul_left.symm,
-      ennreal.tsum_mul_right.symm, mul_assoc, mul_left_comm, mul_comm] using Ennreal.tsum_comm
+      ennreal.tsum_mul_right.symm, mul_assoc, mul_left_comm, mul_comm] using ENNReal.tsum_comm
 #align pmf.bind_bind Pmf.bind_bind
 
 theorem bind_comm (p : Pmf α) (q : Pmf β) (f : α → β → Pmf γ) :
     (p.bind fun a => q.bind (f a)) = q.bind fun b => p.bind fun a => f a b :=
   Pmf.ext fun b => by
     simpa only [ennreal.coe_eq_coe.symm, bind_apply, ennreal.tsum_mul_left.symm,
-      ennreal.tsum_mul_right.symm, mul_assoc, mul_left_comm, mul_comm] using Ennreal.tsum_comm
+      ennreal.tsum_mul_right.symm, mul_assoc, mul_left_comm, mul_comm] using ENNReal.tsum_comm
 #align pmf.bind_comm Pmf.bind_comm
 
 section Measure
@@ -167,8 +167,8 @@ theorem toOuterMeasure_bind_apply :
       simp [to_outer_measure_apply, Set.indicator_apply]
     _ = ∑' (b) (a), p a * if b ∈ s then f a b else 0 := tsum_congr fun b => by split_ifs <;> simp
     _ = ∑' (a) (b), p a * if b ∈ s then f a b else 0 :=
-      tsum_comm' Ennreal.summable (fun _ => Ennreal.summable) fun _ => Ennreal.summable
-    _ = ∑' a, p a * ∑' b, if b ∈ s then f a b else 0 := tsum_congr fun a => Ennreal.tsum_mul_left
+      tsum_comm' ENNReal.summable (fun _ => ENNReal.summable) fun _ => ENNReal.summable
+    _ = ∑' a, p a * ∑' b, if b ∈ s then f a b else 0 := tsum_congr fun a => ENNReal.tsum_mul_left
     _ = ∑' a, p a * ∑' b, if b ∈ s then f a b else 0 :=
       tsum_congr fun a => (congr_arg fun x => p a * x) <| tsum_congr fun b => by split_ifs <;> rfl
     _ = ∑' a, p a * (f a).toOuterMeasure s :=
@@ -201,10 +201,10 @@ section BindOnSupport
   `p.bind f` is equivalent to `p.bind_on_support (λ a _, f a)`, see `bind_on_support_eq_bind` -/
 def bindOnSupport (p : Pmf α) (f : ∀ a ∈ p.support, Pmf β) : Pmf β :=
   ⟨fun b => ∑' a, p a * if h : p a = 0 then 0 else f a h b,
-    Ennreal.summable.hasSum_iff.2
+    ENNReal.summable.hasSum_iff.2
       (by
         refine' ennreal.tsum_comm.trans (trans (tsum_congr fun a => _) p.tsum_coe)
-        simp_rw [Ennreal.tsum_mul_left]
+        simp_rw [ENNReal.tsum_mul_left]
         split_ifs with h
         · simp only [h, zero_mul]
         · rw [(f a h).tsum_coe, mul_one])⟩
@@ -223,7 +223,7 @@ theorem support_bindOnSupport :
     (p.bindOnSupport f).support = ⋃ (a : α) (h : a ∈ p.support), (f a h).support :=
   by
   refine' Set.ext fun b => _
-  simp only [Ennreal.tsum_eq_zero, not_or, mem_support_iff, bind_on_support_apply, Ne.def,
+  simp only [ENNReal.tsum_eq_zero, not_or, mem_support_iff, bind_on_support_apply, Ne.def,
     not_forall, mul_eq_zero, Set.mem_unionᵢ]
   exact
     ⟨fun hb =>
@@ -254,7 +254,7 @@ theorem bindOnSupport_eq_bind (p : Pmf α) (f : α → Pmf β) :
 theorem bindOnSupport_eq_zero_iff (b : β) :
     p.bindOnSupport f b = 0 ↔ ∀ (a) (ha : p a ≠ 0), f a ha b = 0 :=
   by
-  simp only [bind_on_support_apply, Ennreal.tsum_eq_zero, mul_eq_zero, or_iff_not_imp_left]
+  simp only [bind_on_support_apply, ENNReal.tsum_eq_zero, mul_eq_zero, or_iff_not_imp_left]
   exact ⟨fun h a ha => trans (dif_neg ha).symm (h a ha), fun h a ha => trans (dif_neg ha) (h a ha)⟩
 #align pmf.bind_on_support_eq_zero_iff Pmf.bindOnSupport_eq_zero_iff
 
@@ -283,7 +283,7 @@ theorem bindOnSupport_bindOnSupport (p : Pmf α) (f : ∀ a ∈ p.support, Pmf 
   refine' Pmf.ext fun a => _
   simp only [ennreal.coe_eq_coe.symm, bind_on_support_apply, ← tsum_dite_right,
     ennreal.tsum_mul_left.symm, ennreal.tsum_mul_right.symm]
-  simp only [Ennreal.tsum_eq_zero, Ennreal.coe_eq_coe, Ennreal.coe_eq_zero, Ennreal.coe_zero,
+  simp only [ENNReal.tsum_eq_zero, ENNReal.coe_eq_coe, ENNReal.coe_eq_zero, ENNReal.coe_zero,
     dite_eq_left_iff, mul_eq_zero]
   refine' ennreal.tsum_comm.trans (tsum_congr fun a' => tsum_congr fun b => _)
   split_ifs
@@ -301,7 +301,7 @@ theorem bindOnSupport_comm (p : Pmf α) (q : Pmf β) (f : ∀ a ∈ p.support, 
   apply Pmf.ext; rintro c
   simp only [ennreal.coe_eq_coe.symm, bind_on_support_apply, ← tsum_dite_right,
     ennreal.tsum_mul_left.symm, ennreal.tsum_mul_right.symm]
-  refine' trans Ennreal.tsum_comm (tsum_congr fun b => tsum_congr fun a => _)
+  refine' trans ENNReal.tsum_comm (tsum_congr fun b => tsum_congr fun a => _)
   split_ifs with h1 h2 h2 <;> ring
 #align pmf.bind_on_support_comm Pmf.bindOnSupport_comm
 
@@ -322,9 +322,9 @@ theorem toOuterMeasure_bindOnSupport_apply :
         ∑' (b) (a), ite (b ∈ s) (p a * dite (p a = 0) (fun h => 0) fun h => f a h b) 0 :=
       tsum_congr fun b => by split_ifs with hbs <;> simp only [eq_self_iff_true, tsum_zero]
     _ = ∑' (a) (b), ite (b ∈ s) (p a * dite (p a = 0) (fun h => 0) fun h => f a h b) 0 :=
-      Ennreal.tsum_comm
+      ENNReal.tsum_comm
     _ = ∑' a, p a * ∑' b, ite (b ∈ s) (dite (p a = 0) (fun h => 0) fun h => f a h b) 0 :=
-      tsum_congr fun a => by simp only [← Ennreal.tsum_mul_left, mul_ite, mul_zero]
+      tsum_congr fun a => by simp only [← ENNReal.tsum_mul_left, mul_ite, mul_zero]
     _ = ∑' a, p a * dite (p a = 0) (fun h => 0) fun h => ∑' b, ite (b ∈ s) (f a h b) 0 :=
       tsum_congr fun a => by split_ifs with ha <;> simp only [if_t_t, tsum_zero, eq_self_iff_true]
     

mathlib commit https://github.com/leanprover-community/mathlib/commit/c23aca359d4be6975b2a577d5cdb9d77b82c7407

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Devon Tuma
 
 ! This file was ported from Lean 3 source module probability.probability_mass_function.monad
-! leanprover-community/mathlib commit feb165c980c918bb296fede8c3b21dbb4b85bb56
+! leanprover-community/mathlib commit 3f5c9d30716c775bda043456728a1a3ee31412e7
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -30,6 +30,8 @@ variable {α β γ : Type _}
 
 open Classical BigOperators NNReal Ennreal
 
+open MeasureTheory
+
 namespace Pmf
 
 section Pure
@@ -73,13 +75,24 @@ theorem toOuterMeasure_pure_apply : (pure a).toOuterMeasure s = if a ∈ s then
     exact ite_eq_right_iff.2 fun hb => ite_eq_right_iff.2 fun h => (ha <| h ▸ hb).elim
 #align pmf.to_outer_measure_pure_apply Pmf.toOuterMeasure_pure_apply
 
+variable [MeasurableSpace α]
+
 /-- The measure of a set under `pure a` is `1` for sets containing `a` and `0` otherwise -/
 @[simp]
-theorem toMeasure_pure_apply [MeasurableSpace α] (hs : MeasurableSet s) :
+theorem toMeasure_pure_apply (hs : MeasurableSet s) :
     (pure a).toMeasure s = if a ∈ s then 1 else 0 :=
   (toMeasure_apply_eq_toOuterMeasure_apply (pure a) s hs).trans (toOuterMeasure_pure_apply a s)
 #align pmf.to_measure_pure_apply Pmf.toMeasure_pure_apply
 
+theorem toMeasure_pure : (pure a).toMeasure = Measure.dirac a :=
+  Measure.ext fun s hs => by simpa only [to_measure_pure_apply a s hs, measure.dirac_apply' a hs]
+#align pmf.to_measure_pure Pmf.toMeasure_pure
+
+@[simp]
+theorem toPmf_dirac [Countable α] [h : MeasurableSingletonClass α] :
+    (Measure.dirac a).toPmf = pure a := by rw [to_pmf_eq_iff_to_measure_eq, to_measure_pure]
+#align pmf.to_pmf_dirac Pmf.toPmf_dirac
+
 end Measure
 
 end Pure

mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc

Co-authored-by: Moritz Firsching <firsching@google.com>

@@ -172,10 +172,10 @@ theorem toOuterMeasure_bind_apply :
   calc
     (p.bind f).toOuterMeasure s = ∑' b, if b ∈ s then ∑' a, p a * f a b else 0 := by
       simp [toOuterMeasure_apply, Set.indicator_apply]
-    _ = ∑' (b) (a), p a * if b ∈ s then f a b else 0 := (tsum_congr fun b => by split_ifs <;> simp)
+    _ = ∑' (b) (a), p a * if b ∈ s then f a b else 0 := tsum_congr fun b => by split_ifs <;> simp
     _ = ∑' (a) (b), p a * if b ∈ s then f a b else 0 :=
       (tsum_comm' ENNReal.summable (fun _ => ENNReal.summable) fun _ => ENNReal.summable)
-    _ = ∑' a, p a * ∑' b, if b ∈ s then f a b else 0 := (tsum_congr fun a => ENNReal.tsum_mul_left)
+    _ = ∑' a, p a * ∑' b, if b ∈ s then f a b else 0 := tsum_congr fun a => ENNReal.tsum_mul_left
     _ = ∑' a, p a * ∑' b, if b ∈ s then f a b else 0 :=
       (tsum_congr fun a => (congr_arg fun x => p a * x) <| tsum_congr fun b => by split_ifs <;> rfl)
     _ = ∑' a, p a * (f a).toOuterMeasure s :=

@@ -225,7 +225,7 @@ theorem bindOnSupport_apply (b : β) :
 theorem support_bindOnSupport :
     (p.bindOnSupport f).support = ⋃ (a : α) (h : a ∈ p.support), (f a h).support := by
   refine' Set.ext fun b => _
-  simp only [ENNReal.tsum_eq_zero, not_or, mem_support_iff, bindOnSupport_apply, Ne.def, not_forall,
+  simp only [ENNReal.tsum_eq_zero, not_or, mem_support_iff, bindOnSupport_apply, Ne, not_forall,
     mul_eq_zero, Set.mem_iUnion]
   exact
     ⟨fun hb =>

We remove all but one open Classicals, instead preferring to use open scoped Classical. The only real side-effect this led to is moving a couple declarations to use Exists.choose instead of Classical.choose.

The first few commits are explicitly labelled regex replaces for ease of review.

@@ -25,7 +25,8 @@ noncomputable section
 
 variable {α β γ : Type*}
 
-open Classical BigOperators NNReal ENNReal
+open scoped Classical
+open BigOperators NNReal ENNReal
 
 open MeasureTheory
 

Classify by adding issue number (#10618) to porting notes claiming anything semantically equivalent to simp can prove this or simp can simplify this.

@@ -53,7 +53,7 @@ theorem support_pure : (pure a).support = {a} :=
 theorem mem_support_pure_iff : a' ∈ (pure a).support ↔ a' = a := by simp
 #align pmf.mem_support_pure_iff PMF.mem_support_pure_iff
 
--- @[simp] -- Porting note: simp can prove this
+-- @[simp] -- Porting note (#10618): simp can prove this
 theorem pure_apply_self : pure a a = 1 :=
   if_pos rfl
 #align pmf.pure_apply_self PMF.pure_apply_self

by tweaking the definition of the AddMonoid and MonoidWithZero instances for WithTop. Also unprotect ENNReal.coe_injective and rename ENNReal.coe_eq_coe → ENNReal.coe_inj.

From LeanAPAP

@@ -150,14 +150,14 @@ theorem bind_const (p : PMF α) (q : PMF β) : (p.bind fun _ => q) = q :=
 @[simp]
 theorem bind_bind : (p.bind f).bind g = p.bind fun a => (f a).bind g :=
   PMF.ext fun b => by
-    simpa only [ENNReal.coe_eq_coe.symm, bind_apply, ENNReal.tsum_mul_left.symm,
+    simpa only [ENNReal.coe_inj.symm, bind_apply, ENNReal.tsum_mul_left.symm,
       ENNReal.tsum_mul_right.symm, mul_assoc, mul_left_comm, mul_comm] using ENNReal.tsum_comm
 #align pmf.bind_bind PMF.bind_bind
 
 theorem bind_comm (p : PMF α) (q : PMF β) (f : α → β → PMF γ) :
     (p.bind fun a => q.bind (f a)) = q.bind fun b => p.bind fun a => f a b :=
   PMF.ext fun b => by
-    simpa only [ENNReal.coe_eq_coe.symm, bind_apply, ENNReal.tsum_mul_left.symm,
+    simpa only [ENNReal.coe_inj.symm, bind_apply, ENNReal.tsum_mul_left.symm,
       ENNReal.tsum_mul_right.symm, mul_assoc, mul_left_comm, mul_comm] using ENNReal.tsum_comm
 #align pmf.bind_comm PMF.bind_comm
 
@@ -295,7 +295,7 @@ theorem bindOnSupport_comm (p : PMF α) (q : PMF β) (f : ∀ a ∈ p.support, 
     (p.bindOnSupport fun a ha => q.bindOnSupport (f a ha)) =
       q.bindOnSupport fun b hb => p.bindOnSupport fun a ha => f a ha b hb := by
   apply PMF.ext; rintro c
-  simp only [ENNReal.coe_eq_coe.symm, bindOnSupport_apply, ← tsum_dite_right,
+  simp only [ENNReal.coe_inj.symm, bindOnSupport_apply, ← tsum_dite_right,
     ENNReal.tsum_mul_left.symm, ENNReal.tsum_mul_right.symm]
   refine' _root_.trans ENNReal.tsum_comm (tsum_congr fun b => tsum_congr fun a => _)
   split_ifs with h1 h2 h2 <;> ring

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Joachim Breitner <mail@joachim-breitner.de>

@@ -286,7 +286,7 @@ theorem bindOnSupport_bindOnSupport (p : PMF α) (f : ∀ a ∈ p.support, PMF 
   split_ifs with h _ h_1 _ h_2
   any_goals ring1
   · have := h_1 a'
-    simp? [h] at this says simp only [h, dite_false, mul_eq_zero, false_or] at this
+    simp? [h]  at this  says simp only [h, ↓reduceDite, mul_eq_zero, false_or] at this
     contradiction
   · simp [h_2]
 #align pmf.bind_on_support_bind_on_support PMF.bindOnSupport_bindOnSupport

Removes nonterminal uses of simp at. Replaces most of these with instances of simp? ... says.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Mario Carneiro <di.gama@gmail.com>

@@ -286,7 +286,7 @@ theorem bindOnSupport_bindOnSupport (p : PMF α) (f : ∀ a ∈ p.support, PMF 
   split_ifs with h _ h_1 _ h_2
   any_goals ring1
   · have := h_1 a'
-    simp [h] at this
+    simp? [h] at this says simp only [h, dite_false, mul_eq_zero, false_or] at this
     contradiction
   · simp [h_2]
 #align pmf.bind_on_support_bind_on_support PMF.bindOnSupport_bindOnSupport

This eliminates (fun a ↦ β) α in the type when applying a FunLike.

Co-authored-by: Matthew Ballard <matt@mrb.email> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

@@ -130,7 +130,7 @@ theorem mem_support_bind_iff (b : β) :
 @[simp]
 theorem pure_bind (a : α) (f : α → PMF β) : (pure a).bind f = f a := by
   have : ∀ b a', ite (a' = a) (f a' b) 0 = ite (a' = a) (f a b) 0 := fun b a' => by
-    split_ifs with h <;> simp; subst h; simp
+    split_ifs with h <;> simp [h]
   ext b
   simp [this]
 #align pmf.pure_bind PMF.pure_bind

Search and replace Pmf with PMF.

@@ -10,10 +10,10 @@ import Mathlib.Probability.ProbabilityMassFunction.Basic
 /-!
 # Monad Operations for Probability Mass Functions
 
-This file constructs two operations on `Pmf` that give it a monad structure.
+This file constructs two operations on `PMF` that give it a monad structure.
 `pure a` is the distribution where a single value `a` has probability `1`.
-`bind pa pb : Pmf β` is the distribution given by sampling `a : α` from `pa : Pmf α`,
-and then sampling from `pb a : Pmf β` to get a final result `b : β`.
+`bind pa pb : PMF β` is the distribution given by sampling `a : α` from `pa : PMF α`,
+and then sampling from `pb a : PMF β` to get a final result `b : β`.
 
 `bindOnSupport` generalizes `bind` to allow binding to a partial function,
 so that the second argument only needs to be defined on the support of the first argument.
@@ -29,40 +29,40 @@ open Classical BigOperators NNReal ENNReal
 
 open MeasureTheory
 
-namespace Pmf
+namespace PMF
 
 section Pure
 
-/-- The pure `Pmf` is the `Pmf` where all the mass lies in one point.
+/-- The pure `PMF` is the `PMF` where all the mass lies in one point.
   The value of `pure a` is `1` at `a` and `0` elsewhere. -/
-def pure (a : α) : Pmf α :=
+def pure (a : α) : PMF α :=
   ⟨fun a' => if a' = a then 1 else 0, hasSum_ite_eq _ _⟩
-#align pmf.pure Pmf.pure
+#align pmf.pure PMF.pure
 
 variable (a a' : α)
 
 @[simp]
 theorem pure_apply : pure a a' = if a' = a then 1 else 0 := rfl
-#align pmf.pure_apply Pmf.pure_apply
+#align pmf.pure_apply PMF.pure_apply
 
 @[simp]
 theorem support_pure : (pure a).support = {a} :=
   Set.ext fun a' => by simp [mem_support_iff]
-#align pmf.support_pure Pmf.support_pure
+#align pmf.support_pure PMF.support_pure
 
 theorem mem_support_pure_iff : a' ∈ (pure a).support ↔ a' = a := by simp
-#align pmf.mem_support_pure_iff Pmf.mem_support_pure_iff
+#align pmf.mem_support_pure_iff PMF.mem_support_pure_iff
 
 -- @[simp] -- Porting note: simp can prove this
 theorem pure_apply_self : pure a a = 1 :=
   if_pos rfl
-#align pmf.pure_apply_self Pmf.pure_apply_self
+#align pmf.pure_apply_self PMF.pure_apply_self
 
 theorem pure_apply_of_ne (h : a' ≠ a) : pure a a' = 0 :=
   if_neg h
-#align pmf.pure_apply_of_ne Pmf.pure_apply_of_ne
+#align pmf.pure_apply_of_ne PMF.pure_apply_of_ne
 
-instance [Inhabited α] : Inhabited (Pmf α) :=
+instance [Inhabited α] : Inhabited (PMF α) :=
   ⟨pure default⟩
 
 section Measure
@@ -77,7 +77,7 @@ theorem toOuterMeasure_pure_apply : (pure a).toOuterMeasure s = if a ∈ s then
     exact ite_eq_left_iff.2 fun hb => symm (ite_eq_right_iff.2 fun h => (hb <| h.symm ▸ ha).elim)
   · refine' (tsum_congr fun b => _).trans tsum_zero
     exact ite_eq_right_iff.2 fun hb => ite_eq_right_iff.2 fun h => (ha <| h ▸ hb).elim
-#align pmf.to_outer_measure_pure_apply Pmf.toOuterMeasure_pure_apply
+#align pmf.to_outer_measure_pure_apply PMF.toOuterMeasure_pure_apply
 
 variable [MeasurableSpace α]
 
@@ -86,17 +86,17 @@ variable [MeasurableSpace α]
 theorem toMeasure_pure_apply (hs : MeasurableSet s) :
     (pure a).toMeasure s = if a ∈ s then 1 else 0 :=
   (toMeasure_apply_eq_toOuterMeasure_apply (pure a) s hs).trans (toOuterMeasure_pure_apply a s)
-#align pmf.to_measure_pure_apply Pmf.toMeasure_pure_apply
+#align pmf.to_measure_pure_apply PMF.toMeasure_pure_apply
 
 theorem toMeasure_pure : (pure a).toMeasure = Measure.dirac a :=
   Measure.ext fun s hs => by rw [toMeasure_pure_apply a s hs, Measure.dirac_apply' a hs]; rfl
-#align pmf.to_measure_pure Pmf.toMeasure_pure
+#align pmf.to_measure_pure PMF.toMeasure_pure
 
 @[simp]
-theorem toPmf_dirac [Countable α] [h : MeasurableSingletonClass α] :
-    (Measure.dirac a).toPmf = pure a := by
-  rw [toPmf_eq_iff_toMeasure_eq, toMeasure_pure]
-#align pmf.to_pmf_dirac Pmf.toPmf_dirac
+theorem toPMF_dirac [Countable α] [h : MeasurableSingletonClass α] :
+    (Measure.dirac a).toPMF = pure a := by
+  rw [toPMF_eq_iff_toMeasure_eq, toMeasure_pure]
+#align pmf.to_pmf_dirac PMF.toPMF_dirac
 
 end Measure
 
@@ -104,62 +104,62 @@ end Pure
 
 section Bind
 
-/-- The monadic bind operation for `Pmf`. -/
-def bind (p : Pmf α) (f : α → Pmf β) : Pmf β :=
+/-- The monadic bind operation for `PMF`. -/
+def bind (p : PMF α) (f : α → PMF β) : PMF β :=
   ⟨fun b => ∑' a, p a * f a b,
     ENNReal.summable.hasSum_iff.2
       (ENNReal.tsum_comm.trans <| by simp only [ENNReal.tsum_mul_left, tsum_coe, mul_one])⟩
-#align pmf.bind Pmf.bind
+#align pmf.bind PMF.bind
 
-variable (p : Pmf α) (f : α → Pmf β) (g : β → Pmf γ)
+variable (p : PMF α) (f : α → PMF β) (g : β → PMF γ)
 
 @[simp]
 theorem bind_apply (b : β) : p.bind f b = ∑' a, p a * f a b := rfl
-#align pmf.bind_apply Pmf.bind_apply
+#align pmf.bind_apply PMF.bind_apply
 
 @[simp]
 theorem support_bind : (p.bind f).support = ⋃ a ∈ p.support, (f a).support :=
   Set.ext fun b => by simp [mem_support_iff, ENNReal.tsum_eq_zero, not_or]
-#align pmf.support_bind Pmf.support_bind
+#align pmf.support_bind PMF.support_bind
 
 theorem mem_support_bind_iff (b : β) :
     b ∈ (p.bind f).support ↔ ∃ a ∈ p.support, b ∈ (f a).support := by
   simp only [support_bind, Set.mem_iUnion, Set.mem_setOf_eq, exists_prop]
-#align pmf.mem_support_bind_iff Pmf.mem_support_bind_iff
+#align pmf.mem_support_bind_iff PMF.mem_support_bind_iff
 
 @[simp]
-theorem pure_bind (a : α) (f : α → Pmf β) : (pure a).bind f = f a := by
+theorem pure_bind (a : α) (f : α → PMF β) : (pure a).bind f = f a := by
   have : ∀ b a', ite (a' = a) (f a' b) 0 = ite (a' = a) (f a b) 0 := fun b a' => by
     split_ifs with h <;> simp; subst h; simp
   ext b
   simp [this]
-#align pmf.pure_bind Pmf.pure_bind
+#align pmf.pure_bind PMF.pure_bind
 
 @[simp]
 theorem bind_pure : p.bind pure = p :=
-  Pmf.ext fun x => (bind_apply _ _ _).trans (_root_.trans
+  PMF.ext fun x => (bind_apply _ _ _).trans (_root_.trans
     (tsum_eq_single x fun y hy => by rw [pure_apply_of_ne _ _ hy.symm, mul_zero]) <|
     by rw [pure_apply_self, mul_one])
-#align pmf.bind_pure Pmf.bind_pure
+#align pmf.bind_pure PMF.bind_pure
 
 @[simp]
-theorem bind_const (p : Pmf α) (q : Pmf β) : (p.bind fun _ => q) = q :=
-  Pmf.ext fun x => by rw [bind_apply, ENNReal.tsum_mul_right, tsum_coe, one_mul]
-#align pmf.bind_const Pmf.bind_const
+theorem bind_const (p : PMF α) (q : PMF β) : (p.bind fun _ => q) = q :=
+  PMF.ext fun x => by rw [bind_apply, ENNReal.tsum_mul_right, tsum_coe, one_mul]
+#align pmf.bind_const PMF.bind_const
 
 @[simp]
 theorem bind_bind : (p.bind f).bind g = p.bind fun a => (f a).bind g :=
-  Pmf.ext fun b => by
+  PMF.ext fun b => by
     simpa only [ENNReal.coe_eq_coe.symm, bind_apply, ENNReal.tsum_mul_left.symm,
       ENNReal.tsum_mul_right.symm, mul_assoc, mul_left_comm, mul_comm] using ENNReal.tsum_comm
-#align pmf.bind_bind Pmf.bind_bind
+#align pmf.bind_bind PMF.bind_bind
 
-theorem bind_comm (p : Pmf α) (q : Pmf β) (f : α → β → Pmf γ) :
+theorem bind_comm (p : PMF α) (q : PMF β) (f : α → β → PMF γ) :
     (p.bind fun a => q.bind (f a)) = q.bind fun b => p.bind fun a => f a b :=
-  Pmf.ext fun b => by
+  PMF.ext fun b => by
     simpa only [ENNReal.coe_eq_coe.symm, bind_apply, ENNReal.tsum_mul_left.symm,
       ENNReal.tsum_mul_right.symm, mul_assoc, mul_left_comm, mul_comm] using ENNReal.tsum_comm
-#align pmf.bind_comm Pmf.bind_comm
+#align pmf.bind_comm PMF.bind_comm
 
 section Measure
 
@@ -179,7 +179,7 @@ theorem toOuterMeasure_bind_apply :
       (tsum_congr fun a => (congr_arg fun x => p a * x) <| tsum_congr fun b => by split_ifs <;> rfl)
     _ = ∑' a, p a * (f a).toOuterMeasure s :=
       tsum_congr fun a => by simp only [toOuterMeasure_apply, Set.indicator_apply]
-#align pmf.to_outer_measure_bind_apply Pmf.toOuterMeasure_bind_apply
+#align pmf.to_outer_measure_bind_apply PMF.toOuterMeasure_bind_apply
 
 /-- The measure of a set under `p.bind f` is the sum over `a : α`
   of the probability of `a` under `p` times the measure of the set under `f a`. -/
@@ -190,13 +190,13 @@ theorem toMeasure_bind_apply [MeasurableSpace β] (hs : MeasurableSet s) :
     ((toOuterMeasure_bind_apply p f s).trans
       (tsum_congr fun a =>
         congr_arg (fun x => p a * x) (toMeasure_apply_eq_toOuterMeasure_apply (f a) s hs).symm))
-#align pmf.to_measure_bind_apply Pmf.toMeasure_bind_apply
+#align pmf.to_measure_bind_apply PMF.toMeasure_bind_apply
 
 end Measure
 
 end Bind
 
-instance : Monad Pmf where
+instance : Monad PMF where
   pure a := pure a
   bind pa pb := pa.bind pb
 
@@ -204,21 +204,21 @@ section BindOnSupport
 
 /-- Generalized version of `bind` allowing `f` to only be defined on the support of `p`.
   `p.bind f` is equivalent to `p.bindOnSupport (fun a _ ↦ f a)`, see `bindOnSupport_eq_bind`. -/
-def bindOnSupport (p : Pmf α) (f : ∀ a ∈ p.support, Pmf β) : Pmf β :=
+def bindOnSupport (p : PMF α) (f : ∀ a ∈ p.support, PMF β) : PMF β :=
   ⟨fun b => ∑' a, p a * if h : p a = 0 then 0 else f a h b, ENNReal.summable.hasSum_iff.2 (by
     refine' ENNReal.tsum_comm.trans (_root_.trans (tsum_congr fun a => _) p.tsum_coe)
     simp_rw [ENNReal.tsum_mul_left]
     split_ifs with h
     · simp only [h, zero_mul]
     · rw [(f a h).tsum_coe, mul_one])⟩
-#align pmf.bind_on_support Pmf.bindOnSupport
+#align pmf.bind_on_support PMF.bindOnSupport
 
-variable {p : Pmf α} (f : ∀ a ∈ p.support, Pmf β)
+variable {p : PMF α} (f : ∀ a ∈ p.support, PMF β)
 
 @[simp]
 theorem bindOnSupport_apply (b : β) :
     p.bindOnSupport f b = ∑' a, p a * if h : p a = 0 then 0 else f a h b := rfl
-#align pmf.bind_on_support_apply Pmf.bindOnSupport_apply
+#align pmf.bind_on_support_apply PMF.bindOnSupport_apply
 
 @[simp]
 theorem support_bindOnSupport :
@@ -233,52 +233,52 @@ theorem support_bindOnSupport :
       fun hb =>
       let ⟨a, ha, ha'⟩ := hb
       ⟨a, ⟨ha, by simpa [(mem_support_iff _ a).1 ha] using ha'⟩⟩⟩
-#align pmf.support_bind_on_support Pmf.support_bindOnSupport
+#align pmf.support_bind_on_support PMF.support_bindOnSupport
 
 theorem mem_support_bindOnSupport_iff (b : β) :
     b ∈ (p.bindOnSupport f).support ↔ ∃ (a : α) (h : a ∈ p.support), b ∈ (f a h).support := by
   simp only [support_bindOnSupport, Set.mem_setOf_eq, Set.mem_iUnion]
-#align pmf.mem_support_bind_on_support_iff Pmf.mem_support_bindOnSupport_iff
+#align pmf.mem_support_bind_on_support_iff PMF.mem_support_bindOnSupport_iff
 
 /-- `bindOnSupport` reduces to `bind` if `f` doesn't depend on the additional hypothesis. -/
 @[simp]
-theorem bindOnSupport_eq_bind (p : Pmf α) (f : α → Pmf β) :
+theorem bindOnSupport_eq_bind (p : PMF α) (f : α → PMF β) :
     (p.bindOnSupport fun a _ => f a) = p.bind f := by
   ext b
   have : ∀ a, ite (p a = 0) 0 (p a * f a b) = p a * f a b :=
     fun a => ite_eq_right_iff.2 fun h => h.symm ▸ symm (zero_mul <| f a b)
   simp only [bindOnSupport_apply fun a _ => f a, p.bind_apply f, dite_eq_ite, mul_ite,
     mul_zero, this]
-#align pmf.bind_on_support_eq_bind Pmf.bindOnSupport_eq_bind
+#align pmf.bind_on_support_eq_bind PMF.bindOnSupport_eq_bind
 
 theorem bindOnSupport_eq_zero_iff (b : β) :
     p.bindOnSupport f b = 0 ↔ ∀ (a) (ha : p a ≠ 0), f a ha b = 0 := by
   simp only [bindOnSupport_apply, ENNReal.tsum_eq_zero, mul_eq_zero, or_iff_not_imp_left]
   exact ⟨fun h a ha => Trans.trans (dif_neg ha).symm (h a ha),
     fun h a ha => Trans.trans (dif_neg ha) (h a ha)⟩
-#align pmf.bind_on_support_eq_zero_iff Pmf.bindOnSupport_eq_zero_iff
+#align pmf.bind_on_support_eq_zero_iff PMF.bindOnSupport_eq_zero_iff
 
 @[simp]
-theorem pure_bindOnSupport (a : α) (f : ∀ (a' : α) (_ : a' ∈ (pure a).support), Pmf β) :
+theorem pure_bindOnSupport (a : α) (f : ∀ (a' : α) (_ : a' ∈ (pure a).support), PMF β) :
     (pure a).bindOnSupport f = f a ((mem_support_pure_iff a a).mpr rfl) := by
-  refine' Pmf.ext fun b => _
+  refine' PMF.ext fun b => _
   simp only [bindOnSupport_apply, pure_apply]
   refine' _root_.trans (tsum_congr fun a' => _) (tsum_ite_eq a _)
   by_cases h : a' = a <;> simp [h]
-#align pmf.pure_bind_on_support Pmf.pure_bindOnSupport
+#align pmf.pure_bind_on_support PMF.pure_bindOnSupport
 
-theorem bindOnSupport_pure (p : Pmf α) : (p.bindOnSupport fun a _ => pure a) = p := by
-  simp only [Pmf.bind_pure, Pmf.bindOnSupport_eq_bind]
-#align pmf.bind_on_support_pure Pmf.bindOnSupport_pure
+theorem bindOnSupport_pure (p : PMF α) : (p.bindOnSupport fun a _ => pure a) = p := by
+  simp only [PMF.bind_pure, PMF.bindOnSupport_eq_bind]
+#align pmf.bind_on_support_pure PMF.bindOnSupport_pure
 
 @[simp]
-theorem bindOnSupport_bindOnSupport (p : Pmf α) (f : ∀ a ∈ p.support, Pmf β)
-    (g : ∀ b ∈ (p.bindOnSupport f).support, Pmf γ) :
+theorem bindOnSupport_bindOnSupport (p : PMF α) (f : ∀ a ∈ p.support, PMF β)
+    (g : ∀ b ∈ (p.bindOnSupport f).support, PMF γ) :
     (p.bindOnSupport f).bindOnSupport g =
       p.bindOnSupport fun a ha =>
         (f a ha).bindOnSupport fun b hb =>
           g b ((mem_support_bindOnSupport_iff f b).mpr ⟨a, ha, hb⟩) := by
-  refine' Pmf.ext fun a => _
+  refine' PMF.ext fun a => _
   dsimp only [bindOnSupport_apply]
   simp only [← tsum_dite_right, ENNReal.tsum_mul_left.symm, ENNReal.tsum_mul_right.symm]
   simp only [ENNReal.tsum_eq_zero, dite_eq_left_iff]
@@ -289,17 +289,17 @@ theorem bindOnSupport_bindOnSupport (p : Pmf α) (f : ∀ a ∈ p.support, Pmf 
     simp [h] at this
     contradiction
   · simp [h_2]
-#align pmf.bind_on_support_bind_on_support Pmf.bindOnSupport_bindOnSupport
+#align pmf.bind_on_support_bind_on_support PMF.bindOnSupport_bindOnSupport
 
-theorem bindOnSupport_comm (p : Pmf α) (q : Pmf β) (f : ∀ a ∈ p.support, ∀ b ∈ q.support, Pmf γ) :
+theorem bindOnSupport_comm (p : PMF α) (q : PMF β) (f : ∀ a ∈ p.support, ∀ b ∈ q.support, PMF γ) :
     (p.bindOnSupport fun a ha => q.bindOnSupport (f a ha)) =
       q.bindOnSupport fun b hb => p.bindOnSupport fun a ha => f a ha b hb := by
-  apply Pmf.ext; rintro c
+  apply PMF.ext; rintro c
   simp only [ENNReal.coe_eq_coe.symm, bindOnSupport_apply, ← tsum_dite_right,
     ENNReal.tsum_mul_left.symm, ENNReal.tsum_mul_right.symm]
   refine' _root_.trans ENNReal.tsum_comm (tsum_congr fun b => tsum_congr fun a => _)
   split_ifs with h1 h2 h2 <;> ring
-#align pmf.bind_on_support_comm Pmf.bindOnSupport_comm
+#align pmf.bind_on_support_comm PMF.bindOnSupport_comm
 
 section Measure
 
@@ -320,7 +320,7 @@ theorem toOuterMeasure_bindOnSupport_apply :
       (tsum_congr fun a => by simp only [← ENNReal.tsum_mul_left, mul_ite, mul_zero])
     _ = ∑' a, p a * dite (p a = 0) (fun h => 0) fun h => ∑' b, ite (b ∈ s) (f a h b) 0 :=
       tsum_congr fun a => by split_ifs with ha <;> simp only [ite_self, tsum_zero, eq_self_iff_true]
-#align pmf.to_outer_measure_bind_on_support_apply Pmf.toOuterMeasure_bindOnSupport_apply
+#align pmf.to_outer_measure_bind_on_support_apply PMF.toOuterMeasure_bindOnSupport_apply
 
 /-- The measure of a set under `p.bindOnSupport f` is the sum over `a : α`
   of the probability of `a` under `p` times the measure of the set under `f a _`.
@@ -330,10 +330,10 @@ theorem toMeasure_bindOnSupport_apply [MeasurableSpace β] (hs : MeasurableSet s
     (p.bindOnSupport f).toMeasure s =
       ∑' a, p a * if h : p a = 0 then 0 else (f a h).toMeasure s := by
   simp only [toMeasure_apply_eq_toOuterMeasure_apply _ _ hs, toOuterMeasure_bindOnSupport_apply]
-#align pmf.to_measure_bind_on_support_apply Pmf.toMeasure_bindOnSupport_apply
+#align pmf.to_measure_bind_on_support_apply PMF.toMeasure_bindOnSupport_apply
 
 end Measure
 
 end BindOnSupport
 
-end Pmf
+end PMF

Search&replace MulZeroClass.mul_zero -> mul_zero, MulZeroClass.zero_mul -> zero_mul.

These were introduced by Mathport, as the full name of mul_zero is actually MulZeroClass.mul_zero (it's exported with the short name).

@@ -138,7 +138,7 @@ theorem pure_bind (a : α) (f : α → Pmf β) : (pure a).bind f = f a := by
 @[simp]
 theorem bind_pure : p.bind pure = p :=
   Pmf.ext fun x => (bind_apply _ _ _).trans (_root_.trans
-    (tsum_eq_single x fun y hy => by rw [pure_apply_of_ne _ _ hy.symm, MulZeroClass.mul_zero]) <|
+    (tsum_eq_single x fun y hy => by rw [pure_apply_of_ne _ _ hy.symm, mul_zero]) <|
     by rw [pure_apply_self, mul_one])
 #align pmf.bind_pure Pmf.bind_pure
 
@@ -209,7 +209,7 @@ def bindOnSupport (p : Pmf α) (f : ∀ a ∈ p.support, Pmf β) : Pmf β :=
     refine' ENNReal.tsum_comm.trans (_root_.trans (tsum_congr fun a => _) p.tsum_coe)
     simp_rw [ENNReal.tsum_mul_left]
     split_ifs with h
-    · simp only [h, MulZeroClass.zero_mul]
+    · simp only [h, zero_mul]
     · rw [(f a h).tsum_coe, mul_one])⟩
 #align pmf.bind_on_support Pmf.bindOnSupport
 
@@ -246,9 +246,9 @@ theorem bindOnSupport_eq_bind (p : Pmf α) (f : α → Pmf β) :
     (p.bindOnSupport fun a _ => f a) = p.bind f := by
   ext b
   have : ∀ a, ite (p a = 0) 0 (p a * f a b) = p a * f a b :=
-    fun a => ite_eq_right_iff.2 fun h => h.symm ▸ symm (MulZeroClass.zero_mul <| f a b)
+    fun a => ite_eq_right_iff.2 fun h => h.symm ▸ symm (zero_mul <| f a b)
   simp only [bindOnSupport_apply fun a _ => f a, p.bind_apply f, dite_eq_ite, mul_ite,
-    MulZeroClass.mul_zero, this]
+    mul_zero, this]
 #align pmf.bind_on_support_eq_bind Pmf.bindOnSupport_eq_bind
 
 theorem bindOnSupport_eq_zero_iff (b : β) :
@@ -317,7 +317,7 @@ theorem toOuterMeasure_bindOnSupport_apply :
     _ = ∑' (a) (b), ite (b ∈ s) (p a * dite (p a = 0) (fun h => 0) fun h => f a h b) 0 :=
       ENNReal.tsum_comm
     _ = ∑' a, p a * ∑' b, ite (b ∈ s) (dite (p a = 0) (fun h => 0) fun h => f a h b) 0 :=
-      (tsum_congr fun a => by simp only [← ENNReal.tsum_mul_left, mul_ite, MulZeroClass.mul_zero])
+      (tsum_congr fun a => by simp only [← ENNReal.tsum_mul_left, mul_ite, mul_zero])
     _ = ∑' a, p a * dite (p a = 0) (fun h => 0) fun h => ∑' b, ite (b ∈ s) (f a h b) 0 :=
       tsum_congr fun a => by split_ifs with ha <;> simp only [ite_self, tsum_zero, eq_self_iff_true]
 #align pmf.to_outer_measure_bind_on_support_apply Pmf.toOuterMeasure_bindOnSupport_apply

We remove all possible occurences of Type _ and Sort _ in favor of Type* and Sort*.

This has nice performance benefits.

@@ -23,7 +23,7 @@ so that the second argument only needs to be defined on the support of the first
 
 noncomputable section
 
-variable {α β γ : Type _}
+variable {α β γ : Type*}
 
 open Classical BigOperators NNReal ENNReal
 

• depends on: #5966

Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -2,14 +2,11 @@
 Copyright (c) 2020 Devon Tuma. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Devon Tuma
-
-! This file was ported from Lean 3 source module probability.probability_mass_function.monad
-! leanprover-community/mathlib commit 4ac69b290818724c159de091daa3acd31da0ee6d
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Probability.ProbabilityMassFunction.Basic
 
+#align_import probability.probability_mass_function.monad from "leanprover-community/mathlib"@"4ac69b290818724c159de091daa3acd31da0ee6d"
+
 /-!
 # Monad Operations for Probability Mass Functions
 

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Mario Carneiro <di.gama@gmail.com> Co-authored-by: Floris van Doorn <fpvdoorn@gmail.com> Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com> Co-authored-by: Alex J Best <alex.j.best@gmail.com>

@@ -247,7 +247,7 @@ theorem mem_support_bindOnSupport_iff (b : β) :
 @[simp]
 theorem bindOnSupport_eq_bind (p : Pmf α) (f : α → Pmf β) :
     (p.bindOnSupport fun a _ => f a) = p.bind f := by
-  ext (b x)
+  ext b
   have : ∀ a, ite (p a = 0) 0 (p a * f a b) = p a * f a b :=
     fun a => ite_eq_right_iff.2 fun h => h.symm ▸ symm (MulZeroClass.zero_mul <| f a b)
   simp only [bindOnSupport_apply fun a _ => f a, p.bind_apply f, dite_eq_ite, mul_ite,

As discussed on Zulip

Renames

• supₛ → sSup
• infₛ → sInf
• supᵢ → iSup
• infᵢ → iInf
• bsupₛ → bsSup
• binfₛ → bsInf
• bsupᵢ → biSup
• binfᵢ → biInf
• csupₛ → csSup
• cinfₛ → csInf
• csupᵢ → ciSup
• cinfᵢ → ciInf
• unionₛ → sUnion
• interₛ → sInter
• unionᵢ → iUnion
• interᵢ → iInter
• bunionₛ → bsUnion
• binterₛ → bsInter
• bunionᵢ → biUnion
• binterᵢ → biInter

Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>

@@ -127,7 +127,7 @@ theorem support_bind : (p.bind f).support = ⋃ a ∈ p.support, (f a).support :
 
 theorem mem_support_bind_iff (b : β) :
     b ∈ (p.bind f).support ↔ ∃ a ∈ p.support, b ∈ (f a).support := by
-  simp only [support_bind, Set.mem_unionᵢ, Set.mem_setOf_eq, exists_prop]
+  simp only [support_bind, Set.mem_iUnion, Set.mem_setOf_eq, exists_prop]
 #align pmf.mem_support_bind_iff Pmf.mem_support_bind_iff
 
 @[simp]
@@ -228,7 +228,7 @@ theorem support_bindOnSupport :
     (p.bindOnSupport f).support = ⋃ (a : α) (h : a ∈ p.support), (f a h).support := by
   refine' Set.ext fun b => _
   simp only [ENNReal.tsum_eq_zero, not_or, mem_support_iff, bindOnSupport_apply, Ne.def, not_forall,
-    mul_eq_zero, Set.mem_unionᵢ]
+    mul_eq_zero, Set.mem_iUnion]
   exact
     ⟨fun hb =>
       let ⟨a, ⟨ha, ha'⟩⟩ := hb
@@ -240,7 +240,7 @@ theorem support_bindOnSupport :
 
 theorem mem_support_bindOnSupport_iff (b : β) :
     b ∈ (p.bindOnSupport f).support ↔ ∃ (a : α) (h : a ∈ p.support), b ∈ (f a h).support := by
-  simp only [support_bindOnSupport, Set.mem_setOf_eq, Set.mem_unionᵢ]
+  simp only [support_bindOnSupport, Set.mem_setOf_eq, Set.mem_iUnion]
 #align pmf.mem_support_bind_on_support_iff Pmf.mem_support_bindOnSupport_iff
 
 /-- `bindOnSupport` reduces to `bind` if `f` doesn't depend on the additional hypothesis. -/

Co-authored-by: Moritz Firsching <firsching@google.com>