apply Nat.min_eq_right
l : List ℕ
head : ℕ
tail : List ℕ
hyp : head :: tail ≠ []
c : ¬tail = []
c' : ¬head ≤ smallest tail ⋯
⊢ Nat.min head (smallest tail ⋯) = smallest tail ⋯
case h
l : List ℕ
head : ℕ
tail : List ℕ
hyp : head :: tail ≠ []
c : ¬tail = []
c' : ¬head ≤ smallest tail ⋯
⊢ smallest tail ⋯ ≤ head