Theorems · Theorem · functional analysis
CStarAlgebra.inv_le_inv
∀ {A : Type u_1} [inst : CStarAlgebra A] [inst_1 : PartialOrder A] [StarOrderedRing A] {a b : Aˣ},
0 ≤ ↑a → ↑a ≤ ↑b → ↑b⁻¹ ≤ ↑a⁻¹In a unital C⋆-algebra, if 0 ≤ a ≤ b and a and b are units, then b⁻¹ ≤ a⁻¹.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 323 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realproof · cited by 25,697
- PartialOrderstatement and proof · cited by 6,410
- Norm.normproof · cited by 5,413
- LE.le.transproof · cited by 3,151
- Unitsstatement and proof · cited by 2,804
- Units.valstatement and proof · cited by 1,966
- Star.starproof · cited by 1,082
- norm_nonnegproof · cited by 725
- StarOrderedRingstatement and proof · cited by 587
- inv_invproof · cited by 494
- sqproof · cited by 280
- CStarAlgebrastatement and proof · cited by 123
Cited by3
Results whose statement or proof uses this declaration.
- CStarAlgebra.inv_le_inv_iffproof · cited by 2
- CStarAlgebra.antitoneOn_ringInverseproof · cited by 1
- CStarAlgebra.rpow_neg_one_le_rpow_neg_oneproof · cited by 1