Theorems · Theorem · functional analysis
CStarAlgebra.antitoneOn_ringInverse
∀ {A : Type u_1} [inst : CStarAlgebra A] [inst_1 : PartialOrder A] [StarOrderedRing A],
AntitoneOn Ring.inverse {a | IsStrictlyPositive a}- Cited by
- 1 results in Mathlib
- Foundations
- Depth 324 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- Set.ofPredstatement and proof · cited by 6,101
- Units.valproof · cited by 1,966
- StarOrderedRingstatement and proof · cited by 587
- AntitoneOnstatement · cited by 266
- IsUnit.unitproof · cited by 252
- Ring.inversestatement and proof · cited by 160
- CStarAlgebrastatement and proof · cited by 123
- IsStrictlyPositivestatement and proof · cited by 75
- Units.isStrictlyPositive_iffproof · cited by 3
- CStarAlgebra.inv_le_invproof · cited by 3
- Ring.inverse_of_isUnitproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- CStarAlgebra.ringInverse_le_ringInverseproof · cited by 0