Theorems · Theorem · functional analysis
WithAbs.norm_eq_apply_ofAbs
∀ {R : Type u_1} [inst : Ring R] (v : AbsoluteValue R ℝ) (x : WithAbs v), ‖x‖ = v x.ofAbs- Defined in
- Mathlib.Analysis.Normed.Ring.WithAbs
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 127 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Ring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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 and proof · cited by 25,697
- Ringstatement and proof · cited by 7,463
- Norm.normstatement · cited by 5,413
- AbsoluteValuestatement and proof · cited by 363
- WithAbsstatement and proof · cited by 102
- WithAbs.ofAbsstatement · cited by 35
Cited by3
Results whose statement or proof uses this declaration.
- AbsoluteValue.IsEquiv.equivWithAbs_image_mem_nhds_zeroproof · cited by 1
- AbsoluteValue.isEquiv_iff_isHomeomorphproof · cited by 0
- WithAbs.norm_eq_abvproof · cited by 0