Theorems · Theorem · ring theory
OreLocalization.OreSet.ore_right_cancel
∀ {R : Type u_1} {inst : Monoid R} {S : Submonoid R} [self : OreLocalization.OreSet S] (r₁ r₂ : R) (s : ↥S),
r₁ * ↑s = r₂ * ↑s → ∃ s', ↑s' * r₁ = ↑s' * r₂Common factors on the right can be turned into common factors on the left, a weak form of cancellability.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses no axioms
- Assumes
- OreLocalization.OreSet
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Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Monoidstatement and proof · cited by 3,887
- Submonoidstatement and proof · cited by 3,086
- OreLocalization.OreSetstatement and proof · cited by 92
Cited by1
Results whose statement or proof uses this declaration.
- OreLocalization.ore_right_cancelproof · cited by 1