Theorem: inf_mem_of_mem (Sion/ForMathlib/Misc.lean)

State before:
α✝ : Type ?u.7108
α : Type u_1
inst✝ : LinearOrder α
a b : α
s : Set α
ha : a ∈ s
hb : b ∈ s
⊢ a ⊓ b ∈ s
Tactic:
rw [inf_eq_min]
State after:
α✝ : Type ?u.7108
α : Type u_1
inst✝ : LinearOrder α
a b : α
s : Set α
ha : a ∈ s
hb : b ∈ s
⊢ min a b ∈ s

State before:
α✝ : Type ?u.7108
α : Type u_1
inst✝ : LinearOrder α
a b : α
s : Set α
ha : a ∈ s
hb : b ∈ s
⊢ min a b ∈ s
Tactic:
exact min_mem_of_mem ha hb
State after:
no goals