. intro h
  calc
    2^k ≤ 2^n.log2' := Nat.pow_le_pow_of_le_right (by decide) h
    _   ≤ n         := Nat.pow2_log2'_le_self ‹n>0›
case mp
k n : Nat
a✝ : n > 0
⊢ k ≤ log2' n → 2 ^ k ≤ n

case mpr
k n : Nat
a✝ : n > 0
⊢ 2 ^ k ≤ n → k ≤ log2' n
case mpr
k n : Nat
a✝ : n > 0
⊢ 2 ^ k ≤ n → k ≤ log2' n