R : Type u
a b : R
m✝ n✝ : ℕ
inst✝ : Semiring R
p q : R[X]
k l m n : ℕ
u v : R
hu : u ≠ 0
hv : v ≠ 0
⊢ Finsupp.single k u + Finsupp.single l v = Finsupp.single m u + Finsupp.single n v ↔
    k = m ∧ l = n ∨ u = v ∧ k = n ∧ l = m ∨ u + v = 0 ∧ k = l ∧ m = n
R : Type u
a b : R
m✝ n✝ : ℕ
inst✝ : Semiring R
p q : R[X]
k l m n : ℕ
u v : R
hu : u ≠ 0
hv : v ≠ 0
⊢ ↑C u * X ^ k + ↑C v * X ^ l = ↑C u * X ^ m + ↑C v * X ^ n ↔
    k = m ∧ l = n ∨ u = v ∧ k = n ∧ l = m ∨ u + v = 0 ∧ k = l ∧ m = n
simp_rw [C_mul_X_pow_eq_monomial, ← toFinsupp_inj, toFinsupp_add, toFinsupp_monomial]
no goals
R : Type u
a b : R
m✝ n✝ : ℕ
inst✝ : Semiring R
p q : R[X]
k l m n : ℕ
u v : R
hu : u ≠ 0
hv : v ≠ 0
⊢ Finsupp.single k u + Finsupp.single l v = Finsupp.single m u + Finsupp.single n v ↔
    k = m ∧ l = n ∨ u = v ∧ k = n ∧ l = m ∨ u + v = 0 ∧ k = l ∧ m = n
exact Finsupp.single_add_single_eq_single_add_single hu hv