Theorems · Theorem · group theory
AddUnits.isAddUnit_addUnits_add
∀ {M : Type u_3} [inst : AddMonoid M] (u : AddUnits M) (a : M), IsAddUnit (↑u + a) ↔ IsAddUnit aAddition of a u : AddUnits M on the left doesn't affect IsAddUnit.
- Defined in
- Mathlib.Algebra.Group.Units.Defs
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses no axioms
- Assumes
- AddMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- zero_addproof · cited by 2,366
- add_assocproof · cited by 746
- AddUnitsstatement and proof · cited by 325
- AddUnits.valstatement and proof · cited by 248
- IsAddUnitstatement and proof · cited by 215
- AddUnits.neg_addproof · cited by 17
- AddUnits.isAddUnitproof · cited by 14
- IsAddUnit.addproof · cited by 11
- AddUnits.val_addproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- addIrreducible_addUnits_addproof · cited by 1