σ : Type u_1
R : Type u_2
inst✝ : CommSemiring R
φ ψ : MvPolynomial σ R
n : σ →₀ ℕ
a : R
m : σ →₀ ℕ
⊢ (if n = m then a else 0) = if m = n then a else 0
σ : Type u_1
R : Type u_2
inst✝ : CommSemiring R
φ ψ : MvPolynomial σ R
n : σ →₀ ℕ
a : R
m : σ →₀ ℕ
⊢ ↑(MvPowerSeries.coeff R m) ↑(↑(monomial n) a) = ↑(MvPowerSeries.coeff R m) (↑(MvPowerSeries.monomial R n) a)
rw [coeff_coe, coeff_monomial, MvPowerSeries.coeff_monomial]
no goals
σ : Type u_1
R : Type u_2
inst✝ : CommSemiring R
φ ψ : MvPolynomial σ R
n : σ →₀ ℕ
a : R
m : σ →₀ ℕ
⊢ (if n = m then a else 0) = if m = n then a else 0
split_ifs with h₁ h₂ <;> first |rfl|subst m; contradiction
no goals
case inr.inr
σ : Type u_1
R : Type u_2
inst✝ : CommSemiring R
φ ψ : MvPolynomial σ R
n : σ →₀ ℕ
a : R
m : σ →₀ ℕ
h₁ : ¬n = m
h✝ : ¬m = n
⊢ 0 = 0
rfl
case inr.inl
σ : Type u_1
R : Type u_2
inst✝ : CommSemiring R
φ ψ : MvPolynomial σ R
n : σ →₀ ℕ
a : R
h₁ : ¬n = n
⊢ 0 = a
case inr.inl
σ : Type u_1
R : Type u_2
inst✝ : CommSemiring R
φ ψ : MvPolynomial σ R
n : σ →₀ ℕ
a : R
m : σ →₀ ℕ
h₁ : ¬n = m
h✝ : m = n
⊢ 0 = a
subst m
no goals
case inr.inl
σ : Type u_1
R : Type u_2
inst✝ : CommSemiring R
φ ψ : MvPolynomial σ R
n : σ →₀ ℕ
a : R
h₁ : ¬n = n
⊢ 0 = a
contradiction