Theorems · Theorem · functional analysis
InnerProductSpace.Core.norm_inner_le_norm
∀ {𝕜 : Type u_1} {F : Type u_3} [inst : RCLike 𝕜] [inst_1 : AddCommGroup F] [inst_2 : Module 𝕜 F]
[c : PreInnerProductSpace.Core 𝕜 F] (x y : F), ‖inner 𝕜 x y‖ ≤ ‖x‖ * ‖y‖Cauchy–Schwarz inequality with norm
- Defined in
- Mathlib.Analysis.InnerProductSpace.Defs
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 169 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Realstatement and proof · cited by 25,697
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Norm.normstatement and proof · cited by 5,413
- RCLikestatement and proof · cited by 2,829
- Inner.innerstatement and proof · cited by 1,089
- mul_nonnegproof · cited by 397
- RCLike.reproof · cited by 319
- PreInnerProductSpace.Corestatement and proof · cited by 46
- Real.sqrt_nonnegproof · cited by 35
- InnerProductSpace.Core.toPreInner'statement · cited by 32
Cited by1
Results whose statement or proof uses this declaration.
- norm_inner_le_normproof · cited by 14