Mathlib Map

Theorems · Inductive type · commutative algebra

IsAddRegular

{R : Type u_2} → [Add R] → R → Prop

An add-regular element is an element c such that addition by c both on the left and on the right is injective.

Defined in
Mathlib.Algebra.Regular.Defs
Cited by
43 results in Mathlib
Foundations
Depth 1 from the axioms · uses no axioms
Assumes
Add
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

IsAddRegular.left · cited by 8IsAddRegular.leftisAddRegular_iff · cited by 7isAddRegular_iffIsAddRegular.right · cited by 7IsAddRegular.rightAddCommute.isAddRegular_iff · cited by 3AddCommute.isAddRegular_i…IsAddRegular.of_ne_top · cited by 3IsAddRegular.of_ne_topisAddRegular_add_and_add_iff · cited by 2isAddRegular_add_and_add_…isAddRegular_add_iff · cited by 2isAddRegular_add_iffisAddRegular_op · cited by 2isAddRegular_opisAddRegular_zero · cited by 2isAddRegular_zeroisCancelAdd_iff_forall_isAddRegular · cited by 2isCancelAdd_iff_forall_is…isAddLeftRegular_iff_isAddRegular · cited by 1isAddLeftRegular_iff_isAd…Prod.isAddRegular_mk · cited by 1Prod.isAddRegular_mkAddSubmonoid.LocalizationMap.injective_iff · cited by 1LocalizationMap.injective…AddSubmonoid.LocalizationMap.map_isAddRegular · cited by 1LocalizationMap.map_isAdd…AddUnits.isAddRegular · cited by 1AddUnits.isAddRegularIsAddRegularCITED BYCITES

Cites0

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

Nothing in Mathlib beyond the foundations.

Cited by45

Results whose statement or proof uses this declaration.