Theorems · Theorem · functional analysis
CStarModule.norm_triangle
∀ (A : Type u_1) {E : Type u_2} [inst : NonUnitalCStarAlgebra A] [inst_1 : PartialOrder A] [inst_2 : AddCommGroup E]
[inst_3 : Module ℂ E] [inst_4 : SMul A E] [inst_5 : Norm E] [CStarModule A E] [StarOrderedRing A] (x y : E),
‖x + y‖ ≤ ‖x‖ + ‖y‖- Cited by
- 1 results in Mathlib
- Foundations
- Depth 322 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites27
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- PartialOrderstatement and proof · cited by 6,410
- Complexstatement and proof · cited by 5,565
- Norm.normstatement and proof · cited by 5,413
- le_reflproof · cited by 2,061
- StarRingproof · cited by 1,686
- Inner.innerproof · cited by 1,089
- add_le_addproof · cited by 666
- StarOrderedRingstatement and proof · cited by 587
- Real.sqrtproof · cited by 545
Cited by1
Results whose statement or proof uses this declaration.
- CStarModule.normedSpaceCoreproof · cited by 1