Theorem: Set.union_subset_union_left (GMLInit/Data/Set/Subset.lean)

State before:
α : Sort u_1
s t u : Set α
⊢ s.Subset t → ∀ (u : Set α), (u.union s).Subset (u.union t)
Tactic:
intro hst u x
State after:
α : Sort u_1
s t u✝ : Set α
hst : s.Subset t
u : Set α
x : α
⊢ x ∈ u.union s → x ∈ u.union t

State before:
α : Sort u_1
s t u✝ : Set α
hst : s.Subset t
u : Set α
x : α
⊢ x ∈ u.union s → x ∈ u.union t
Tactic:
intro
| Or.inl hu =>
  left
  exact hu
| Or.inr hs =>
  right
  exact hst x hs
State after:
no goals

State before:
α : Sort u_1
s t u✝ : Set α
hst : s.Subset t
u : Set α
x : α
x✝ : x ∈ u.union s
hu : x ∈ u
⊢ x ∈ u.union t
Tactic:
left
State after:
case h
α : Sort u_1
s t u✝ : Set α
hst : s.Subset t
u : Set α
x : α
x✝ : x ∈ u.union s
hu : x ∈ u
⊢ x ∈ u

State before:
case h
α : Sort u_1
s t u✝ : Set α
hst : s.Subset t
u : Set α
x : α
x✝ : x ∈ u.union s
hu : x ∈ u
⊢ x ∈ u
Tactic:
exact hu
State after:
no goals

State before:
α : Sort u_1
s t u✝ : Set α
hst : s.Subset t
u : Set α
x : α
x✝ : x ∈ u.union s
hs : x ∈ s
⊢ x ∈ u.union t
Tactic:
right
State after:
case h
α : Sort u_1
s t u✝ : Set α
hst : s.Subset t
u : Set α
x : α
x✝ : x ∈ u.union s
hs : x ∈ s
⊢ x ∈ t

State before:
case h
α : Sort u_1
s t u✝ : Set α
hst : s.Subset t
u : Set α
x : α
x✝ : x ∈ u.union s
hs : x ∈ s
⊢ x ∈ t
Tactic:
exact hst x hs
State after:
no goals