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

State before:
α : Sort u_1
β : ?m.13185
γ : ?m.13188
s : Set α
⊢ s.inter Set.empty = Set.empty
Tactic:
apply Set.ext
State after:
case a
α : Sort u_1
β : ?m.13185
γ : ?m.13188
s : Set α
⊢ ∀ (x : α), x ∈ s.inter Set.empty ↔ x ∈ Set.empty

State before:
case a
α : Sort u_1
β : ?m.13185
γ : ?m.13188
s : Set α
⊢ ∀ (x : α), x ∈ s.inter Set.empty ↔ x ∈ Set.empty
Tactic:
intro x
State after:
case a
α : Sort u_1
β : ?m.13185
γ : ?m.13188
s : Set α
x : α
⊢ x ∈ s.inter Set.empty ↔ x ∈ Set.empty

State before:
case a
α : Sort u_1
β : ?m.13185
γ : ?m.13188
s : Set α
x : α
⊢ x ∈ s.inter Set.empty ↔ x ∈ Set.empty
Tactic:
constructor
State after:
case a.mp
α : Sort u_1
β : ?m.13185
γ : ?m.13188
s : Set α
x : α
⊢ x ∈ s.inter Set.empty → x ∈ Set.empty

case a.mpr
α : Sort u_1
β : ?m.13185
γ : ?m.13188
s : Set α
x : α
⊢ x ∈ Set.empty → x ∈ s.inter Set.empty

State before:
case a.mp
α : Sort u_1
β : ?m.13185
γ : ?m.13188
s : Set α
x : α
⊢ x ∈ s.inter Set.empty → x ∈ Set.empty
Tactic:
intro ⟨_, _⟩
State after:
case a.mp
α : Sort u_1
β : ?m.13185
γ : ?m.13188
s : Set α
x : α
left✝ : x ∈ s
right✝ : x ∈ Set.empty
⊢ x ∈ Set.empty

State before:
case a.mp
α : Sort u_1
β : ?m.13185
γ : ?m.13188
s : Set α
x : α
left✝ : x ∈ s
right✝ : x ∈ Set.empty
⊢ x ∈ Set.empty
Tactic:
assumption
State after:
no goals

State before:
case a.mpr
α : Sort u_1
β : ?m.13185
γ : ?m.13188
s : Set α
x : α
⊢ x ∈ Set.empty → x ∈ s.inter Set.empty
Tactic:
intro _
State after:
case a.mpr
α : Sort u_1
β : ?m.13185
γ : ?m.13188
s : Set α
x : α
a✝ : x ∈ Set.empty
⊢ x ∈ s.inter Set.empty

State before:
case a.mpr
α : Sort u_1
β : ?m.13185
γ : ?m.13188
s : Set α
x : α
a✝ : x ∈ Set.empty
⊢ x ∈ s.inter Set.empty
Tactic:
contradiction
State after:
no goals