Theorems · Theorem · group theory
isCancelAdd_iff_forall_isAddRegular
∀ {R : Type u_2} [inst : Add R], IsCancelAdd R ↔ ∀ (r : R), IsAddRegular r- Defined in
- Mathlib.Algebra.Group.Defs
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses propext
- Assumes
- Add
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- IsCancelAddstatement · cited by 79
- IsRightCancelAddproof · cited by 69
- IsAddLeftRegularproof · cited by 58
- IsAddRegularstatement and proof · cited by 43
- isAddRegular_iffproof · cited by 7
- isRightCancelAdd_iffproof · cited by 2
- isLeftCancelAdd_iffproof · cited by 2
- isCancelAdd_iffproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- AddSubmonoid.LocalizationMap.isCancelAddproof · cited by 0
- AddSubmonoid.LocalizationMap.top_injective_iffproof · cited by 0