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

State before:
α : Sort u_2
β : Sort u_1
γ : ?m.13535
f : α → β
⊢ Set.map f Set.empty = Set.empty
Tactic:
apply Set.ext
State after:
case a
α : Sort u_2
β : Sort u_1
γ : ?m.13535
f : α → β
⊢ ∀ (x : β), x ∈ Set.map f Set.empty ↔ x ∈ Set.empty

State before:
case a
α : Sort u_2
β : Sort u_1
γ : ?m.13535
f : α → β
⊢ ∀ (x : β), x ∈ Set.map f Set.empty ↔ x ∈ Set.empty
Tactic:
intro x
State after:
case a
α : Sort u_2
β : Sort u_1
γ : ?m.13535
f : α → β
x : β
⊢ x ∈ Set.map f Set.empty ↔ x ∈ Set.empty

State before:
case a
α : Sort u_2
β : Sort u_1
γ : ?m.13535
f : α → β
x : β
⊢ x ∈ Set.map f Set.empty ↔ x ∈ Set.empty
Tactic:
constructor
State after:
case a.mp
α : Sort u_2
β : Sort u_1
γ : ?m.13535
f : α → β
x : β
⊢ x ∈ Set.map f Set.empty → x ∈ Set.empty

case a.mpr
α : Sort u_2
β : Sort u_1
γ : ?m.13535
f : α → β
x : β
⊢ x ∈ Set.empty → x ∈ Set.map f Set.empty

State before:
case a.mp
α : Sort u_2
β : Sort u_1
γ : ?m.13535
f : α → β
x : β
⊢ x ∈ Set.map f Set.empty → x ∈ Set.empty
Tactic:
intro ⟨_,_,_⟩
State after:
case a.mp
α : Sort u_2
β : Sort u_1
γ : ?m.13535
f : α → β
x : β
w✝ : α
left✝ : w✝ ∈ Set.empty
right✝ : f w✝ = x
⊢ x ∈ Set.empty

State before:
case a.mp
α : Sort u_2
β : Sort u_1
γ : ?m.13535
f : α → β
x : β
w✝ : α
left✝ : w✝ ∈ Set.empty
right✝ : f w✝ = x
⊢ x ∈ Set.empty
Tactic:
contradiction
State after:
no goals

State before:
case a.mpr
α : Sort u_2
β : Sort u_1
γ : ?m.13535
f : α → β
x : β
⊢ x ∈ Set.empty → x ∈ Set.map f Set.empty
Tactic:
intro _
State after:
case a.mpr
α : Sort u_2
β : Sort u_1
γ : ?m.13535
f : α → β
x : β
a✝ : x ∈ Set.empty
⊢ x ∈ Set.map f Set.empty

State before:
case a.mpr
α : Sort u_2
β : Sort u_1
γ : ?m.13535
f : α → β
x : β
a✝ : x ∈ Set.empty
⊢ x ∈ Set.map f Set.empty
Tactic:
contradiction
State after:
no goals