Theorems · Theorem · commutative algebra
IsAddRightRegular.of_add
∀ {R : Type u_1} [inst : AddSemigroup R] {a b : R}, IsAddRightRegular (b + a) → IsAddRightRegular bIf an element b becomes add-right-regular after adding to it on the right
an add-right-regular element, then b is add-right-regular.
- Defined in
- Mathlib.Algebra.Regular.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
- Assumes
- AddSemigroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- add_assocproof · cited by 746
- AddSemigroupstatement and proof · cited by 136
- IsAddRightRegularstatement and proof · cited by 55
Cited by5
Results whose statement or proof uses this declaration.
- isAddRegular_add_and_add_iffproof · cited by 2
- isAddRightRegular_of_add_eq_zeroproof · cited by 2
- IsAddRightRegular.nsmul_iffproof · cited by 1
- AddSubmonoid.LocalizationMap.isCancelAddproof · cited by 0
- add_isAddRightRegular_iffproof · cited by 0