case h_X
σ : Type u_1
τ : Type u_3
α : Type ?u.592987
R : Type u_2
S : Type ?u.592993
inst✝¹ : CommSemiring R
inst✝ : CommSemiring S
f : R →+* S
k : σ → τ
g✝ : τ → S
p : MvPolynomial σ R
j : τ
g : σ → MvPolynomial σ R
p✝ : MvPolynomial σ R
n✝ : σ
a✝ : ↑(rename (Prod.mk j)) (eval₂ C g p✝) = eval₂ C (fun x => ↑(rename (Prod.mk j)) (g x)) p✝
⊢ ↑(rename (Prod.mk j)) (eval₂ C g (p✝ * X n✝)) = eval₂ C (fun x => ↑(rename (Prod.mk j)) (g x)) (p✝ * X n✝)
case h_X
σ : Type u_1
τ : Type u_3
α : Type ?u.592987
R : Type u_2
S : Type ?u.592993
inst✝¹ : CommSemiring R
inst✝ : CommSemiring S
f : R →+* S
k : σ → τ
g✝ : τ → S
p : MvPolynomial σ R
j : τ
g : σ → MvPolynomial σ R
⊢ ∀ (p : MvPolynomial σ R) (n : σ),
    ↑(rename (Prod.mk j)) (eval₂ C g p) = eval₂ C (fun x => ↑(rename (Prod.mk j)) (g x)) p →
      ↑(rename (Prod.mk j)) (eval₂ C g (p * X n)) = eval₂ C (fun x => ↑(rename (Prod.mk j)) (g x)) (p * X n)
intros
no goals
case h_X
σ : Type u_1
τ : Type u_3
α : Type ?u.592987
R : Type u_2
S : Type ?u.592993
inst✝¹ : CommSemiring R
inst✝ : CommSemiring S
f : R →+* S
k : σ → τ
g✝ : τ → S
p : MvPolynomial σ R
j : τ
g : σ → MvPolynomial σ R
p✝ : MvPolynomial σ R
n✝ : σ
a✝ : ↑(rename (Prod.mk j)) (eval₂ C g p✝) = eval₂ C (fun x => ↑(rename (Prod.mk j)) (g x)) p✝
⊢ ↑(rename (Prod.mk j)) (eval₂ C g (p✝ * X n✝)) = eval₂ C (fun x => ↑(rename (Prod.mk j)) (g x)) (p✝ * X n✝)
simp [*]