Theorem: Measurable.iInf_Prop
File: Mathlib/MeasureTheory/Constructions/BorelSpace/Order.lean

tactic: simp_rw [ciInf_eq_ite]
state_before: α✝ : Type u_1
β : Type u_2
γ : Type u_3
δ : Type u_4
ι : Sort y
s t u : Set α✝
inst✝⁸ : TopologicalSpace α✝
inst✝⁷ : MeasurableSpace α✝
inst✝⁶ : BorelSpace α✝
inst✝⁵ : TopologicalSpace β
inst✝⁴ : MeasurableSpace β
inst✝³ : BorelSpace β
inst✝² : MeasurableSpace δ
α : Type u_5
inst✝¹ : MeasurableSpace α
inst✝ : ConditionallyCompleteLattice α
p : Prop
f : δ → α
hf : Measurable f
⊢ Measurable fun b => ⨅ (_ : p), f b
state_after: α✝ : Type u_1
β : Type u_2
γ : Type u_3
δ : Type u_4
ι : Sort y
s t u : Set α✝
inst✝⁸ : TopologicalSpace α✝
inst✝⁷ : MeasurableSpace α✝
inst✝⁶ : BorelSpace α✝
inst✝⁵ : TopologicalSpace β
inst✝⁴ : MeasurableSpace β
inst✝³ : BorelSpace β
inst✝² : MeasurableSpace δ
α : Type u_5
inst✝¹ : MeasurableSpace α
inst✝ : ConditionallyCompleteLattice α
p : Prop
f : δ → α
hf : Measurable f
⊢ Measurable fun b => if h : p then f b else sInf ∅

tactic: split_ifs with h
state_before: α✝ : Type u_1
β : Type u_2
γ : Type u_3
δ : Type u_4
ι : Sort y
s t u : Set α✝
inst✝⁸ : TopologicalSpace α✝
inst✝⁷ : MeasurableSpace α✝
inst✝⁶ : BorelSpace α✝
inst✝⁵ : TopologicalSpace β
inst✝⁴ : MeasurableSpace β
inst✝³ : BorelSpace β
inst✝² : MeasurableSpace δ
α : Type u_5
inst✝¹ : MeasurableSpace α
inst✝ : ConditionallyCompleteLattice α
p : Prop
f : δ → α
hf : Measurable f
⊢ Measurable fun b => if h : p then f b else sInf ∅
state_after: case pos
α✝ : Type u_1
β : Type u_2
γ : Type u_3
δ : Type u_4
ι : Sort y
s t u : Set α✝
inst✝⁸ : TopologicalSpace α✝
inst✝⁷ : MeasurableSpace α✝
inst✝⁶ : BorelSpace α✝
inst✝⁵ : TopologicalSpace β
inst✝⁴ : MeasurableSpace β
inst✝³ : BorelSpace β
inst✝² : MeasurableSpace δ
α : Type u_5
inst✝¹ : MeasurableSpace α
inst✝ : ConditionallyCompleteLattice α
p : Prop
f : δ → α
hf : Measurable f
h : p
⊢ Measurable fun b => f b

case neg
α✝ : Type u_1
β : Type u_2
γ : Type u_3
δ : Type u_4
ι : Sort y
s t u : Set α✝
inst✝⁸ : TopologicalSpace α✝
inst✝⁷ : MeasurableSpace α✝
inst✝⁶ : BorelSpace α✝
inst✝⁵ : TopologicalSpace β
inst✝⁴ : MeasurableSpace β
inst✝³ : BorelSpace β
inst✝² : MeasurableSpace δ
α : Type u_5
inst✝¹ : MeasurableSpace α
inst✝ : ConditionallyCompleteLattice α
p : Prop
f : δ → α
hf : Measurable f
h : ¬p
⊢ Measurable fun b => sInf ∅

tactic: exact hf
state_before: case pos
α✝ : Type u_1
β : Type u_2
γ : Type u_3
δ : Type u_4
ι : Sort y
s t u : Set α✝
inst✝⁸ : TopologicalSpace α✝
inst✝⁷ : MeasurableSpace α✝
inst✝⁶ : BorelSpace α✝
inst✝⁵ : TopologicalSpace β
inst✝⁴ : MeasurableSpace β
inst✝³ : BorelSpace β
inst✝² : MeasurableSpace δ
α : Type u_5
inst✝¹ : MeasurableSpace α
inst✝ : ConditionallyCompleteLattice α
p : Prop
f : δ → α
hf : Measurable f
h : p
⊢ Measurable fun b => f b
state_after: no goals

tactic: exact measurable_const
state_before: case neg
α✝ : Type u_1
β : Type u_2
γ : Type u_3
δ : Type u_4
ι : Sort y
s t u : Set α✝
inst✝⁸ : TopologicalSpace α✝
inst✝⁷ : MeasurableSpace α✝
inst✝⁶ : BorelSpace α✝
inst✝⁵ : TopologicalSpace β
inst✝⁴ : MeasurableSpace β
inst✝³ : BorelSpace β
inst✝² : MeasurableSpace δ
α : Type u_5
inst✝¹ : MeasurableSpace α
inst✝ : ConditionallyCompleteLattice α
p : Prop
f : δ → α
hf : Measurable f
h : ¬p
⊢ Measurable fun b => sInf ∅
state_after: no goals