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

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

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

case right
α : Sort u_1
s t u✝ : Set α
hst : s.Subset t
u : Set α
x : α
hs : x ∈ s
hu : x ∈ u
⊢ x ∈ u

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

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