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Theorems · Theorem · group theory

IsDedekindFiniteAddMonoid.add_eq_zero_symm

∀ {M : Type u_2} {inst : AddZero M} [self : IsDedekindFiniteAddMonoid M] {a b : M}, a + b = 0 → b + a = 0
Defined in
Mathlib.Algebra.Group.Defs
Cited by
4 results in Mathlib
Foundations
Depth 4 from the axioms · uses no axioms
Assumes
IsDedekindFiniteAddMonoid
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Around this declaration

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

IsAddUnit.of_add_eq_zero_right · cited by 1IsAddUnit.of_add_eq_zero_…add_eq_zero_comm · cited by 1add_eq_zero_commIsDedekindFiniteAddMonoid.iff_isAddLeftRegular_of_add_eq_zero · cited by 0IsDedekindFiniteAddMonoid…IsDedekindFiniteAddMonoid.iff_isAddRightRegular_of_add_eq_zero · cited by 0IsDedekindFiniteAddMonoid…AddZero · cited by 87AddZeroIsDedekindFiniteAddMonoid · cited by 18IsDedekindFiniteAddMonoidIsDedekindFiniteAddMonoid.add…CITED BYCITES

Cites2

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Cited by4

Results whose statement or proof uses this declaration.