case intro
R : Type u_1
inst✝ : CommSemiring R
p : R[X]
hp : Monic p
r : R
q : R[X]
h : p = ↑C r * q
⊢ IsUnit r
R : Type u_1
inst✝ : CommSemiring R
p : R[X]
hp : Monic p
⊢ IsPrimitive p
rintro r ⟨q, h⟩
no goals
case intro
R : Type u_1
inst✝ : CommSemiring R
p : R[X]
hp : Monic p
r : R
q : R[X]
h : p = ↑C r * q
⊢ IsUnit r
exact isUnit_of_mul_eq_one r (q.coeff p.natDegree) (by rwa [← coeff_C_mul, ← h])
no goals
R : Type u_1
inst✝ : CommSemiring R
p : R[X]
hp : Monic p
r : R
q : R[X]
h : p = ↑C r * q
⊢ r * coeff q (natDegree p) = 1
rwa [← coeff_C_mul, ← h]