eq_zero — Mathlib

English

Given a division of 0 by g, the quotient and remainder are both zero.

Русский

При делении нуля на g, частное и остаток равны нулю.

LaTeX

$$If (q,r) satisfy IsWeierstrassDivision 0 g q r, then q = 0 and r = 0.$$

Lean4

/-- If `q` and `r` are quotient and remainder in the Weierstrass division `0 / g`, then they are
equal to `0`. -/
theorem eq_zero [IsHausdorff (IsLocalRing.maximalIdeal A) A] {q : A⟦X⟧} {r : A[X]} (H : IsWeierstrassDivision 0 g q r) :
    q = 0 ∧ r = 0 :=
  H.elim hg (g.isWeierstrassDivisionAt_zero _)

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