Mathlib Map

Theorems · Theorem · group theory

GroupWithZero.inv_zero

∀ {G₀ : Type u} [self : GroupWithZero G₀], 0⁻¹ = 0

The inverse of 0 in a group with zero is 0.

Defined in
Mathlib.Algebra.GroupWithZero.Defs
Cited by
3 results in Mathlib
Foundations
Depth 4 from the axioms · uses no axioms
Assumes
GroupWithZero
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

inv_zero · cited by 184inv_zeroEReal.inv_zero · cited by 4EReal.inv_zeroFintype.divisionRingOfIsDomain · cited by 1Fintype.divisionRingOfIsD…CauSeq.Completion.ofRat_inv · cited by 1Completion.ofRat_invcommGroupWithZeroOfIsUnitOrEqZero · cited by 0commGroupWithZeroOfIsUnit…Function.Injective.divisionRing · cited by 0Injective.divisionRingFunction.Injective.commGroupWithZero · cited by 0Injective.commGroupWithZe…Function.Injective.divisionSemiring · cited by 0Injective.divisionSemiringDivisionRing.ofIsUnitOrEqZero · cited by 0DivisionRing.ofIsUnitOrEq…Function.Surjective.commGroupWithZero · cited by 0Surjective.commGroupWithZ…GroupWithZero · cited by 691GroupWithZeroMonoidWithZero.toZero · cited by 8MonoidWithZero.toZeroGroupWithZero.toInv · cited by 4GroupWithZero.toInvGroupWithZero.inv_zeroCITED BYCITES

Cites3

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Cited by10

Results whose statement or proof uses this declaration.