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

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

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

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

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