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

State before:
α : Sort u_1
β : ?m.4818
γ : ?m.4821
s : Set α
⊢ Set.map id s = s
Tactic:
apply Set.ext
State after:
case a
α : Sort u_1
β : ?m.4818
γ : ?m.4821
s : Set α
⊢ ∀ (x : α), x ∈ Set.map id s ↔ x ∈ s

State before:
case a
α : Sort u_1
β : ?m.4818
γ : ?m.4821
s : Set α
⊢ ∀ (x : α), x ∈ Set.map id s ↔ x ∈ s
Tactic:
intro x
State after:
case a
α : Sort u_1
β : ?m.4818
γ : ?m.4821
s : Set α
x : α
⊢ x ∈ Set.map id s ↔ x ∈ s

State before:
case a
α : Sort u_1
β : ?m.4818
γ : ?m.4821
s : Set α
x : α
⊢ x ∈ Set.map id s ↔ x ∈ s
Tactic:
constructor
State after:
case a.mp
α : Sort u_1
β : ?m.4818
γ : ?m.4821
s : Set α
x : α
⊢ x ∈ Set.map id s → x ∈ s

case a.mpr
α : Sort u_1
β : ?m.4818
γ : ?m.4821
s : Set α
x : α
⊢ x ∈ s → x ∈ Set.map id s

State before:
case a.mp
α : Sort u_1
β : ?m.4818
γ : ?m.4821
s : Set α
x : α
⊢ x ∈ Set.map id s → x ∈ s
Tactic:
intro ⟨_, hx, rfl⟩
State after:
case a.mp
α : Sort u_1
β : ?m.4818
γ : ?m.4821
s : Set α
x : α
hx : x ∈ s
⊢ x ∈ s

State before:
case a.mp
α : Sort u_1
β : ?m.4818
γ : ?m.4821
s : Set α
x : α
hx : x ∈ s
⊢ x ∈ s
Tactic:
exact hx
State after:
no goals

State before:
case a.mpr
α : Sort u_1
β : ?m.4818
γ : ?m.4821
s : Set α
x : α
⊢ x ∈ s → x ∈ Set.map id s
Tactic:
intro hx
State after:
case a.mpr
α : Sort u_1
β : ?m.4818
γ : ?m.4821
s : Set α
x : α
hx : x ∈ s
⊢ x ∈ Set.map id s

State before:
case a.mpr
α : Sort u_1
β : ?m.4818
γ : ?m.4821
s : Set α
x : α
hx : x ∈ s
⊢ x ∈ Set.map id s
Tactic:
refine ⟨x, hx, rfl⟩
State after:
no goals