Theorems · Theorem · general topology
IsUltrametricDist.isNonarchimedean_norm
∀ {R : Type u_4} [inst : SeminormedAddCommGroup R] [IsUltrametricDist R], IsNonarchimedean fun x => ‖x‖- Defined in
- Mathlib.Analysis.Normed.Group.Ultra
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Norm.normstatement and proof · cited by 5,413
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- zero_addproof · cited by 2,366
- Dist.distproof · cited by 1,539
- neg_zeroproof · cited by 542
- IsUltrametricDiststatement and proof · cited by 177
- neg_add_cancel_leftproof · cited by 84
- IsNonarchimedeanstatement · cited by 77
- dist_zeroproof · cited by 16
- IsUltrametricDist.dist_triangle_maxproof · cited by 8
- SeminormedAddGroup.dist_eqproof · cited by 3
Cited by8
Results whose statement or proof uses this declaration.
- spectralNorm_eq_invariantExtensionproof · cited by 3
- IsUltrametricDist.algNormOfAlgEquiv_extendsproof · cited by 1
- IsUltrametricDist.isNonarchimedean_algNormOfAlgEquivproof · cited by 1
- IsUltrametricDist.isPowMul_algNormOfAlgEquivproof · cited by 1
- IsUltrametricDist.algNormOfAlgEquiv_applystatement · cited by 0
- IsUltrametricDist.isNonarchimedean_nnnormproof · cited by 0
- IsUltrametricDist.isUltrametricDist_iff_isNonarchimedean_nnnormproof · cited by 0
- IsUltrametricDist.isUltrametricDist_iff_isNonarchimedean_normproof · cited by 0