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Theorems · Definition · ring theory

OreLocalization.oreNum

{R : Type u_1} → [inst : Monoid R] → {S : Submonoid R} → [OreLocalization.OreSet S] → R → ↥S → R

The Ore numerator of a fraction.

Defined in
Mathlib.GroupTheory.OreLocalization.OreSet
Cited by
11 results in Mathlib
Foundations
Depth 12 from the axioms · uses no axioms
Assumes
MonoidOreLocalization.OreSet
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

OreLocalization.oreDivAddChar' · cited by 4OreLocalization.oreDivAdd…OreLocalization.oreDiv_smul_oreDiv · cited by 3OreLocalization.oreDiv_sm…OreLocalization.smul_oreDiv · cited by 3OreLocalization.smul_oreD…OreLocalization.oreCondition · cited by 2OreLocalization.oreCondit…OreLocalization.oreDivSMulChar' · cited by 2OreLocalization.oreDivSMu…OreLocalization.oreDiv_add_oreDiv · cited by 2OreLocalization.oreDiv_ad…OreLocalization.ore_eq · cited by 2OreLocalization.ore_eqOreLocalization.nonempty_oreSet_iff_of_noZeroDivisors · cited by 1OreLocalization.nonempty_…OreLocalization.oreDivMulChar' · cited by 1OreLocalization.oreDivMul…OreLocalization.oreDiv_mul_oreDiv · cited by 1OreLocalization.oreDiv_mu…OreLocalization.oreDiv_one_smul · cited by 1OreLocalization.oreDiv_on…OreLocalization.smul_add · cited by 1OreLocalization.smul_addOreLocalization.smul_one_smul · cited by 1OreLocalization.smul_one_…OreLocalization.hsmul · cited by 0OreLocalization.hsmulOreLocalization.oreSetComm_oreNum · cited by 0OreLocalization.oreSetCom…Monoid · cited by 3887MonoidSubmonoid · cited by 3086SubmonoidOreLocalization.OreSet · cited by 92OreLocalization.OreSetOreLocalization.OreSet.oreNum · cited by 1OreSet.oreNumOreLocalization.oreNumCITED BYCITES

Cites4

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by16

Results whose statement or proof uses this declaration.