Theorems · Theorem · ring theory
IsUnit.mem_unitary_iff_star_mul_self
∀ {R : Type u_1} [inst : Monoid R] [inst_1 : StarMul R] {u : R}, IsUnit u → (u ∈ unitary R ↔ star u * u = 1)- Defined in
- Mathlib.Algebra.Star.Unitary
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 23 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.
- Monoidstatement and proof · cited by 3,887
- Submonoidstatement · cited by 3,086
- Unitsproof · cited by 2,804
- Units.valproof · cited by 1,966
- IsUnitstatement and proof · cited by 1,602
- Star.starstatement and proof · cited by 1,082
- unitarystatement · cited by 207
- StarMulstatement and proof · cited by 195
- Units.mul_invproof · cited by 67
- left_inv_eq_right_invproof · cited by 19
- Unitary.mem_iffproof · cited by 7
Cited by3
Results whose statement or proof uses this declaration.
- IsUnit.mem_unitary_iff_mul_star_selfproof · cited by 1
- Unitary.mul_inv_mem_iffproof · cited by 1
- IsUnit.mem_unitary_of_star_mul_selfproof · cited by 0