Theorems · Theorem · functional analysis
CFC.inv_nonneg_of_nonneg
∀ {A : Type u_1} [inst : TopologicalSpace A] [inst_1 : Ring A] [inst_2 : StarRing A] [inst_3 : PartialOrder A]
[inst_4 : Algebra NNReal A] [ContinuousFunctionalCalculus NNReal A fun x => 0 ≤ x] (a : Aˣ),
autoParam (0 ≤ ↑a) CFC.inv_nonneg_of_nonneg._auto_1 → 0 ≤ ↑a⁻¹- Cited by
- 5 results in Mathlib
- Foundations
- Depth 155 from the axioms · uses propext, Classical.choice, 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.
- TopologicalSpacestatement and proof · cited by 24,529
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- PartialOrderstatement and proof · cited by 6,410
- NNRealstatement and proof · cited by 4,310
- Unitsstatement and proof · cited by 2,804
- Units.valstatement and proof · cited by 1,966
- StarRingstatement and proof · cited by 1,686
- ContinuousFunctionalCalculusstatement and proof · cited by 331
- cfc_predicateproof · cited by 6
- cfc_inv_idproof · cited by 5
Cited by5
Results whose statement or proof uses this declaration.
- CStarAlgebra.inv_le_invproof · cited by 3
- CStarAlgebra.inv_le_inv_iffproof · cited by 2
- CStarAlgebra.inv_le_iffproof · cited by 1
- CStarAlgebra.le_inv_iffproof · cited by 1
- CFC.inv_nonnegproof · cited by 0