Theorems · Theorem · functional analysis
UniformSpace.Completion.norm_coe
∀ {E : Type u_2} [inst : SeminormedAddCommGroup E] (x : E), ‖↑x‖ = ‖x‖- Defined in
- Mathlib.Analysis.Normed.Group.Completion
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 159 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SeminormedAddCommGroup
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.
- Realstatement · cited by 25,697
- Norm.normstatement · cited by 5,413
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- UniformSpace.Completionstatement · cited by 192
- UniformSpace.Completion.coe'statement · cited by 144
- UniformSpace.Completion.extension_coeproof · cited by 8
- uniformContinuous_normproof · cited by 4
Cited by18
Results whose statement or proof uses this declaration.
- UniformSpace.Completion.toComplₗᵢproof · cited by 5
- UniformSpace.Completion.nnnorm_coeproof · cited by 2
- NormedAddGroupHom.norm_completionproof · cited by 2
- Complex.affine_of_mapsTo_ball_of_norm_dslope_eq_divproof · cited by 2
- Asymptotics.isBigO_completion_leftproof · cited by 2
- Asymptotics.isBigO_completion_rightproof · cited by 2
- PadicComplex.norm_extendsproof · cited by 1
- Complex.norm_deriv_le_of_forall_mem_sphere_norm_leproof · cited by 1
- norm_sub_le_integral_of_norm_deriv_le_of_leproof · cited by 1
- NumberField.InfinitePlace.Completion.norm_coeproof · cited by 1
- Complex.norm_max_aux₂proof · cited by 1
- PadicComplex.norm_extends'proof · cited by 0