obtain (k|k) := k
case some.some
K : Type u_1
p : ℕ+
hpri : Fact p.Prime
inst✝² : Field K
inst✝¹ : CharZero K
inst✝ : IsCyclotomicExtension {p} ℚ K
ζ : K
hζ : IsPrimitiveRoot ζ ↑p
k : ℕ∞
hk : k ≠ 0
hk' : k ≠ ⊤
n m : ℕ
⊢ k * some n ≤ k * some m ↔ some n ≤ some m
case some.some.none
K : Type u_1
p : ℕ+
hpri : Fact p.Prime
inst✝² : Field K
inst✝¹ : CharZero K
inst✝ : IsCyclotomicExtension {p} ℚ K
ζ : K
hζ : IsPrimitiveRoot ζ ↑p
n m : ℕ
hk : none ≠ 0
hk' : none ≠ ⊤
⊢ none * some n ≤ none * some m ↔ some n ≤ some m

case some.some.some
K : Type u_1
p : ℕ+
hpri : Fact p.Prime
inst✝² : Field K
inst✝¹ : CharZero K
inst✝ : IsCyclotomicExtension {p} ℚ K
ζ : K
hζ : IsPrimitiveRoot ζ ↑p
n m k : ℕ
hk : some k ≠ 0
hk' : some k ≠ ⊤
⊢ some k * some n ≤ some k * some m ↔ some n ≤ some m