Theorems · Theorem · group theory
irreducible_mul_units
∀ {M : Type u_2} [inst : Monoid M] {y : M} (u : Mˣ), Irreducible (y * ↑u) ↔ Irreducible y- Defined in
- Mathlib.Algebra.Group.Irreducible.Lemmas
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses propext
- Assumes
- Monoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- mul_assocproof · cited by 1,667
- IsUnitproof · cited by 1,602
- Irreduciblestatement · cited by 496
- Units.mul_inv_cancel_rightproof · cited by 20
- Units.isUnit_mul_unitsproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- irreducible_mul_isUnitproof · cited by 2