Mathlib Map

Theorems · Theorem · group theory

IsAddUnit.add_iff

∀ {M : Type u_1} [inst : AddMonoid M] [IsDedekindFiniteAddMonoid M] {x y : M},
  IsAddUnit (x + y) ↔ IsAddUnit x ∧ IsAddUnit y
Defined in
Mathlib.Algebra.Group.Units.Defs
Cited by
2 results in Mathlib
Foundations
Depth 12 from the axioms · uses no axioms
Assumes
AddMonoidIsDedekindFiniteAddMonoid
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

List.sum_isAddUnit_iff · cited by 0List.sum_isAddUnit_iffIsAddUnit.multisetSum_iff · cited by 0IsAddUnit.multisetSum_iffAddMonoid · cited by 2864AddMonoidIsAddUnit · cited by 215IsAddUnitIsDedekindFiniteAddMonoid · cited by 18IsDedekindFiniteAddMonoidIsAddUnit.add · cited by 11IsAddUnit.addisAddUnit_of_add_isAddUnit_left · cited by 1isAddUnit_of_add_isAddUni…isAddUnit_of_add_isAddUnit_right · cited by 1isAddUnit_of_add_isAddUni…IsAddUnit.add_iffCITED BYCITES

Cites6

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

Cited by2

Results whose statement or proof uses this declaration.