Mathlib Map

Theorems · Theorem · group theory

AddUnits.val_neg

∀ {α : Type u} [inst : AddMonoid α] (self : AddUnits α), ↑self + self.neg = 0

neg is the right additive inverse of val in the base AddMonoid.

Defined in
Mathlib.Algebra.Group.Units.Defs
Cited by
3 results in Mathlib
Foundations
Depth 6 from the axioms · uses no axioms
Assumes
AddMonoid
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

AddUnits.add_neg · cited by 19AddUnits.add_negisAddUnit_iff_exists · cited by 3isAddUnit_iff_existsNat.addUnits_eq_zero · cited by 0Nat.addUnits_eq_zeroAddMonoid · cited by 2864AddMonoidAddUnits · cited by 325AddUnitsAddUnits.val · cited by 248AddUnits.valAddUnits.neg · cited by 14AddUnits.negAddUnits.val_negCITED BYCITES

Cites4

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by3

Results whose statement or proof uses this declaration.