Theorems · Theorem · group theory
Units.isUnit_units_mul
∀ {M : Type u_3} [inst : Monoid M] (u : Mˣ) (a : M), IsUnit (↑u * a) ↔ IsUnit aMultiplication by a u : Mˣ on the left doesn't affect IsUnit.
- Defined in
- Mathlib.Algebra.Group.Units.Defs
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses no axioms
- Assumes
- Monoid
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.
- Monoidstatement and proof · cited by 3,887
- one_mulproof · cited by 2,841
- Unitsstatement and proof · cited by 2,804
- Units.valstatement and proof · cited by 1,966
- mul_assocproof · cited by 1,667
- IsUnitstatement and proof · cited by 1,602
- Units.isUnitproof · cited by 116
- Units.inv_mulproof · cited by 46
- IsUnit.mulproof · cited by 32
- Units.val_mulproof · cited by 22
Cited by4
Results whose statement or proof uses this declaration.
- IsLocalRing.isUnit_or_isUnit_of_isUnit_addproof · cited by 4
- IsUnit.isStrictlyPositive_star_right_conjugate_iffproof · cited by 1
- irreducible_units_mulproof · cited by 1
- FractionalIdeal.isUnit_numproof · cited by 0