derivativeFinsupp_one — Mathlib

English

For any p ∈ R[X], derivativeFinsupp(derivative p) equals the comapDomain of derivativeFinsupp p along Nat.succ, i.e., shifting indices by one.

Русский

Для любого p ∈ R[X] derivativeFinsupp(derivative p) равен cometDomain derivativeFinsupp p по Nat.succ, т.е. сдвиг индексов на единицу.

LaTeX

$$$$ \mathrm{derivativeFinsupp}(\mathrm{derivative}(p)) = \mathrm{comapDomain}_{\mathrm{Nat.succ}}(\mathrm{derivativeFinsupp}(p)) $$$$

Lean4

@[simp]
theorem derivativeFinsupp_one : derivativeFinsupp (1 : R[X]) = .single 0 1 := by simpa using derivativeFinsupp_C (1 : R)

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