Theorems · Theorem · functional analysis
CStarAlgebra.inr_mem_Icc_iff_norm_le
∀ {A : Type u_1} [inst : NonUnitalCStarAlgebra A] [inst_1 : PartialOrder A] [StarOrderedRing A] {x : A},
↑x ∈ Set.Icc 0 1 ↔ 0 ≤ x ∧ ‖x‖ ≤ 1- Cited by
- 1 results in Mathlib
- Foundations
- Depth 321 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- PartialOrderstatement and proof · cited by 6,410
- Complexstatement · cited by 5,565
- Norm.normstatement and proof · cited by 5,413
- Set.Iccstatement · cited by 1,702
- StarOrderedRingstatement and proof · cited by 587
- Unitizationstatement · cited by 220
- NonUnitalCStarAlgebrastatement and proof · cited by 149
- Unitization.inrstatement and proof · cited by 109
- Unitization.inr_nonneg_iffproof · cited by 8
- Unitization.norm_inrproof · cited by 8
Cited by1
Results whose statement or proof uses this declaration.
- CStarAlgebra.inr_mem_Icc_iff_nnnorm_leproof · cited by 0