Theorems · Theorem · functional analysis
Unitization.norm_def
∀ {𝕜 : Type u_1} {A : Type u_2} [inst : NontriviallyNormedField 𝕜] [inst_1 : NonUnitalNormedRing A]
[inst_2 : NormedSpace 𝕜 A] [inst_3 : IsScalarTower 𝕜 A A] [inst_4 : SMulCommClass 𝕜 A A]
[inst_5 : RegularNormedAlgebra 𝕜 A] (x : Unitization 𝕜 A), ‖x‖ = ‖(Unitization.splitMul 𝕜 A) x‖- Cited by
- 1 results in Mathlib
- Foundations
- Depth 184 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.coestatement · cited by 62,936
- Realstatement · cited by 25,697
- RingHom.idstatement · cited by 18,349
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Norm.normstatement · cited by 5,413
- ContinuousLinearMapstatement · cited by 5,352
- IsScalarTowerstatement and proof · cited by 3,896
- AlgHomstatement · cited by 3,236
- SMulCommClassstatement and proof · cited by 1,927
- NonUnitalNormedRingstatement and proof · cited by 231
- Unitizationstatement and proof · cited by 220
Cited by1
Results whose statement or proof uses this declaration.
- Unitization.norm_eq_supproof · cited by 4