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

State before:
α : Sort u_1
s t u : Set α
⊢ s.Subset t → t.Subset u → s.Subset u
Tactic:
intro hst htu x hs
State after:
α : Sort u_1
s t u : Set α
hst : s.Subset t
htu : t.Subset u
x : α
hs : x ∈ s
⊢ x ∈ u

State before:
α : Sort u_1
s t u : Set α
hst : s.Subset t
htu : t.Subset u
x : α
hs : x ∈ s
⊢ x ∈ u
Tactic:
apply htu
State after:
case a
α : Sort u_1
s t u : Set α
hst : s.Subset t
htu : t.Subset u
x : α
hs : x ∈ s
⊢ x ∈ t

State before:
case a
α : Sort u_1
s t u : Set α
hst : s.Subset t
htu : t.Subset u
x : α
hs : x ∈ s
⊢ x ∈ t
Tactic:
apply hst
State after:
case a.a
α : Sort u_1
s t u : Set α
hst : s.Subset t
htu : t.Subset u
x : α
hs : x ∈ s
⊢ x ∈ s

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