Theorems · Theorem · functional analysis
CStarAlgebra.le_inv_iff
∀ {A : Type u_1} [inst : CStarAlgebra A] [inst_1 : PartialOrder A] [StarOrderedRing A] {a b : Aˣ},
0 ≤ ↑a → 0 ≤ ↑b → (↑a ≤ ↑b⁻¹ ↔ ↑b ≤ ↑a⁻¹)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 325 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- PartialOrderstatement and proof · cited by 6,410
- Unitsstatement and proof · cited by 2,804
- Units.valstatement and proof · cited by 1,966
- StarOrderedRingstatement and proof · cited by 587
- inv_invproof · cited by 494
- CStarAlgebrastatement and proof · cited by 123
- CFC.inv_nonneg_of_nonnegproof · cited by 5
- CStarAlgebra.inv_le_inv_iffproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- CStarAlgebra.one_le_inv_iff_le_oneproof · cited by 0