Theorems · Theorem · commutative algebra
Submonoid.inv_mem_of_isUnit
∀ {α : Type u_2} {C : Type u_4} [inst : SetLike C α] [inst_1 : DivisionMonoid α] [inst_2 : SubmonoidClass C α] {S : C}
{a : ↥S}, IsUnit a → (↑a)⁻¹ ∈ S- Defined in
- Mathlib.RingTheory.Ideal.Nonunits
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Unitsproof · cited by 2,804
- Units.valproof · cited by 1,966
- IsUnitstatement and proof · cited by 1,602
- SetLikestatement and proof · cited by 1,084
- MonoidHom.compproof · cited by 469
- DivisionMonoidstatement and proof · cited by 201
- map_invproof · cited by 95
- SubmonoidClassstatement and proof · cited by 60
- Units.coeHomproof · cited by 44
- Submonoid.subtypeproof · cited by 26
- Submonoid.ofClassproof · cited by 6
Cited by2
Results whose statement or proof uses this declaration.
- Submonoid.isUnit_iff_andproof · cited by 2
- Submonoid.isUnit_iffproof · cited by 1