ι : Sort ?u.7990
M : Type u_1
A : Type ?u.7996
B : Type ?u.7999
inst✝ : Mul M
S T : Subsemigroup M
this : T ≤ S ⊔ T
⊢ ∀ {x : M}, x ∈ T → x ∈ S ⊔ T
ι : Sort ?u.7990
M : Type u_1
A : Type ?u.7996
B : Type ?u.7999
inst✝ : Mul M
S T : Subsemigroup M
⊢ ∀ {x : M}, x ∈ T → x ∈ S ⊔ T
have : T ≤ S ⊔ T := le_sup_right
no goals
ι : Sort ?u.7990
M : Type u_1
A : Type ?u.7996
B : Type ?u.7999
inst✝ : Mul M
S T : Subsemigroup M
this : T ≤ S ⊔ T
⊢ ∀ {x : M}, x ∈ T → x ∈ S ⊔ T
tauto