Theorems · Theorem · commutative algebra
IsDedekindFiniteAddMonoid.iff_isAddLeftRegular_of_add_eq_zero
∀ {R : Type u_1} [inst : AddMonoid R], IsDedekindFiniteAddMonoid R ↔ ∀ (x y : R), x + y = 0 → IsAddLeftRegular x- Defined in
- Mathlib.Algebra.Regular.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses propext, Quot.sound
- Assumes
- AddMonoid
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Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddMonoidstatement and proof · cited by 2,864
- add_zeroproof · cited by 2,707
- zero_addproof · cited by 2,366
- add_assocproof · cited by 746
- IsAddLeftRegularstatement and proof · cited by 58
- IsDedekindFiniteAddMonoidstatement and proof · cited by 18
- IsDedekindFiniteAddMonoid.add_eq_zero_symmproof · cited by 4
- isAddLeftRegular_of_add_eq_zeroproof · cited by 2
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