homogenize_monomial — Mathlib

English

In NoZeroSMulDivisors Nat R, natDegree hasseDeriv n p equals natDegree p minus n.

Русский

При отсутствии нулевых делителей Nat R, natDegree(hasseDeriv_n p) = natDegree(p) − n.

LaTeX

$$$\operatorname{natDegree}(\mathrm{hasseDeriv}_n p) = \operatorname{natDegree}(p) - n$$$

Lean4

@[simp]
theorem homogenize_monomial {m n : ℕ} (h : m ≤ n) (r : R) :
    homogenize (monomial m r) n = .monomial (fun₀ | 0 => m | 1 => n - m) r :=
  by
  rw [homogenize, Finset.sum_eq_single (a := (m, n - m))]
  · simp
  · aesop (add simp coeff_monomial)
  · simp [h]

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