Theorems · Theorem · group theory
isUnit_iff_eq_one
∀ {M : Type u_1} [inst : Monoid M] {a : M} [Subsingleton Mˣ], IsUnit a ↔ a = 1- Defined in
- Mathlib.Algebra.Group.Units.Defs
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses propext
- Assumes
- MonoidSubsingleton
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
- IsUnitstatement · cited by 1,602
- isUnit_oneproof · cited by 48
- IsUnit.eq_oneproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- Nat.isUnit_iffproof · cited by 7
- AddSubgroup.index_dvd_two_iffproof · cited by 2
- AddMonoid.exponent_eq_prime_iffproof · cited by 1
- IsUnit.orderOf_eq_oneproof · cited by 0