Theorems · Theorem · general topology
IsUltrametricDist.isUltrametricDist_of_forall_norm_add_le_max_norm
∀ {S' : Type u_2} [inst : SeminormedAddGroup S'], (∀ (x y : S'), ‖x + y‖ ≤ max ‖x‖ ‖y‖) → IsUltrametricDist S'- Defined in
- Mathlib.Analysis.Normed.Group.Ultra
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SeminormedAddGroup
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 and proof · cited by 5,413
- SeminormedAddGroupstatement and proof · cited by 331
- IsUltrametricDiststatement · cited by 177
- dist_eq_norm_neg_addproof · cited by 46
- le_sup_iffproof · cited by 7
- add_add_neg_add_cancelproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- IsUltrametricDist.isUltrametricDist_of_isNonarchimedean_normproof · cited by 2
- IsUltrametricDist.isUltrametricDist_of_forall_nnnorm_add_le_max_nnnormproof · cited by 1