Theorem: Set.inter_comm (GMLInit/Data/Set/Basic.lean)

State before:
α : Sort u_1
β : ?m.20207
γ : ?m.20210
s t : Set α
⊢ s.inter t = t.inter s
Tactic:
apply Set.ext
State after:
case a
α : Sort u_1
β : ?m.20207
γ : ?m.20210
s t : Set α
⊢ ∀ (x : α), x ∈ s.inter t ↔ x ∈ t.inter s

State before:
case a
α : Sort u_1
β : ?m.20207
γ : ?m.20210
s t : Set α
⊢ ∀ (x : α), x ∈ s.inter t ↔ x ∈ t.inter s
Tactic:
intro x
State after:
case a
α : Sort u_1
β : ?m.20207
γ : ?m.20210
s t : Set α
x : α
⊢ x ∈ s.inter t ↔ x ∈ t.inter s

State before:
case a
α : Sort u_1
β : ?m.20207
γ : ?m.20210
s t : Set α
x : α
⊢ x ∈ s.inter t ↔ x ∈ t.inter s
Tactic:
constructor
State after:
case a.mp
α : Sort u_1
β : ?m.20207
γ : ?m.20210
s t : Set α
x : α
⊢ x ∈ s.inter t → x ∈ t.inter s

case a.mpr
α : Sort u_1
β : ?m.20207
γ : ?m.20210
s t : Set α
x : α
⊢ x ∈ t.inter s → x ∈ s.inter t

State before:
case a.mp
α : Sort u_1
β : ?m.20207
γ : ?m.20210
s t : Set α
x : α
⊢ x ∈ s.inter t → x ∈ t.inter s
Tactic:
intro ⟨hs, ht⟩
State after:
case a.mp
α : Sort u_1
β : ?m.20207
γ : ?m.20210
s t : Set α
x : α
hs : x ∈ s
ht : x ∈ t
⊢ x ∈ t.inter s

State before:
case a.mp
α : Sort u_1
β : ?m.20207
γ : ?m.20210
s t : Set α
x : α
hs : x ∈ s
ht : x ∈ t
⊢ x ∈ t.inter s
Tactic:
exact ⟨ht, hs⟩
State after:
no goals

State before:
case a.mpr
α : Sort u_1
β : ?m.20207
γ : ?m.20210
s t : Set α
x : α
⊢ x ∈ t.inter s → x ∈ s.inter t
Tactic:
intro ⟨ht, hs⟩
State after:
case a.mpr
α : Sort u_1
β : ?m.20207
γ : ?m.20210
s t : Set α
x : α
ht : x ∈ t
hs : x ∈ s
⊢ x ∈ s.inter t

State before:
case a.mpr
α : Sort u_1
β : ?m.20207
γ : ?m.20210
s t : Set α
x : α
ht : x ∈ t
hs : x ∈ s
⊢ x ∈ s.inter t
Tactic:
exact ⟨hs, ht⟩
State after:
no goals