Theorems · Theorem · functional analysis
WithLp.unitization_norm_def
∀ {𝕜 : Type u_1} {A : Type u_2} [inst : NormedField 𝕜] [inst_1 : NonUnitalNormedRing A] [inst_2 : NormedSpace 𝕜 A]
(x : WithLp 1 (Unitization 𝕜 A)), ‖x‖ = ‖x.ofLp.toProd.1‖ + ‖x.ofLp.toProd.2‖- Cited by
- 2 results in Mathlib
- Foundations
- Depth 224 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.
- DFunLike.coeproof · cited by 62,936
- Realstatement · cited by 25,697
- NormedSpacestatement and proof · cited by 12,499
- ENNRealstatement · cited by 9,879
- Norm.normstatement and proof · cited by 5,413
- NormedFieldstatement and proof · cited by 1,084
- WithLpstatement and proof · cited by 345
- WithLp.ofLpstatement and proof · cited by 323
- div_selfproof · cited by 237
- NonUnitalNormedRingstatement and proof · cited by 231
- Unitizationstatement and proof · cited by 220
- Real.rpow_oneproof · cited by 114
Cited by2
Results whose statement or proof uses this declaration.
- WithLp.unitization_nnnorm_defproof · cited by 1
- WithLp.unitization_norm_inrproof · cited by 1