Theorem: Tutorial.isOpen_empty (LCTutorial/Solutions/Topics/GaloisAdjunctions.lean)

State before:
X : Type
T : Topology X
⊢ Topology.isOpen T ∅
Tactic:
have : (∅ : Set X) = ⋃ i : Empty, i.rec
State after:
case this
X : Type
T : Topology X
⊢ ∅ = ⋃ (i : Empty), Empty.rec (fun x => Set X) i

X : Type
T : Topology X
this : ∅ = ⋃ (i : Empty), Empty.rec (fun x => Set X) i
⊢ Topology.isOpen T ∅

State before:
X : Type
T : Topology X
this : ∅ = ⋃ (i : Empty), Empty.rec (fun x => Set X) i
⊢ Topology.isOpen T ∅
Tactic:
rw [this]
State after:
X : Type
T : Topology X
this : ∅ = ⋃ (i : Empty), Empty.rec (fun x => Set X) i
⊢ Topology.isOpen T (⋃ (i : Empty), Empty.rec (fun x => Set X) i)

State before:
X : Type
T : Topology X
this : ∅ = ⋃ (i : Empty), Empty.rec (fun x => Set X) i
⊢ Topology.isOpen T (⋃ (i : Empty), Empty.rec (fun x => Set X) i)
Tactic:
exact T.isOpen_iUnion Empty.rec
State after:
no goals

State before:
case this
X : Type
T : Topology X
⊢ ∅ = ⋃ (i : Empty), Empty.rec (fun x => Set X) i
Tactic:
rw [Set.iUnion_of_empty]
State after:
no goals