Theorems · Theorem · functional analysis
CStarAlgebra.norm_le_norm_of_nonneg_of_le
∀ {A : Type u_1} [inst : NonUnitalCStarAlgebra A] [inst_1 : PartialOrder A] [StarOrderedRing A] {a b : A},
autoParam (0 ≤ a) CStarAlgebra.norm_le_norm_of_nonneg_of_le._auto_1 → a ≤ b → ‖a‖ ≤ ‖b‖- Cited by
- 6 results in Mathlib
- Foundations
- Depth 320 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- PartialOrderstatement and proof · cited by 6,410
- Complexproof · cited by 5,565
- Norm.normstatement and proof · cited by 5,413
- LE.le.transproof · cited by 3,151
- norm_nonnegproof · cited by 725
- StarOrderedRingstatement and proof · cited by 587
- Unitizationproof · cited by 220
- NonUnitalCStarAlgebrastatement and proof · cited by 149
- Unitization.inrproof · cited by 109
- IsSelfAdjoint.of_nonnegproof · cited by 43
- Unitization.inr_le_iffproof · cited by 8
Cited by6
Results whose statement or proof uses this declaration.
- CStarModule.norm_inner_leproof · cited by 2
- WithCStarModule.norm_apply_le_normproof · cited by 2
- WithCStarModule.max_le_prod_normproof · cited by 1
- CStarAlgebra.nnnorm_le_nnnorm_of_nonneg_of_leproof · cited by 1
- PositiveLinearMap.exists_norm_apply_leproof · cited by 0
- PositiveLinearMap.norm_apply_le_of_nonnegproof · cited by 0