ore_right_cancel — Mathlib

English

If r1 s = r2 s for some s ∈ S, then there exists s' ∈ S with s' r1 = s' r2.

Русский

Если r1 s = r2 s и s ∈ S, то существует s' ∈ S such that s' r1 = s' r2.

LaTeX

$$∃ s' : S, s' r1 = s' r2$$

Lean4

/-- Common factors on the right can be turned into common factors on the left, a weak form of
cancellability. -/
@[to_additive AddOreLocalization.ore_right_cancel]
theorem ore_right_cancel (r₁ r₂ : R) (s : S) (h : r₁ * s = r₂ * s) : ∃ s' : S, s' * r₁ = s' * r₂ :=
  OreSet.ore_right_cancel r₁ r₂ s h

Похожие утверждения