Theorems · Theorem · group theory
Units.isUnit_mul_units
∀ {M : Type u_1} [inst : Monoid M] (a : M) (u : Mˣ), IsUnit (a * ↑u) ↔ IsUnit aMultiplication by a u : Mˣ on the right doesn't affect IsUnit.
- Defined in
- Mathlib.Algebra.Group.Units.Defs
- Cited by
- 3 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
- mul_oneproof · cited by 3,885
- 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.mul_invproof · cited by 67
- IsUnit.mulproof · cited by 32
- Units.val_mulproof · cited by 22
Cited by3
Results whose statement or proof uses this declaration.
- IsNilpotent.isUnit_add_left_of_commuteproof · cited by 4
- irreducible_mul_unitsproof · cited by 1
- IsUnit.isStrictlyPositive_star_right_conjugate_iffproof · cited by 1