Theorems · Definition · group theory
Units.rightOfMul
{M : Type u_1} → [inst : Monoid M] → (u : Mˣ) → (a b : M) → a * b = ↑u → Commute a b → MˣIf the product of two commuting elements is a unit, then the right multiplier is a unit.
- Defined in
- Mathlib.Algebra.Group.Commute.Units
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext
- Assumes
- Monoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- Unitsstatement and proof · cited by 2,804
- Units.valstatement and proof · cited by 1,966
- Commutestatement and proof · cited by 639
- Units.leftOfMulproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Commute.isUnit_mul_iffproof · cited by 9