Theorems · Theorem · general topology
IsUltrametricDist.norm_mul_le_max
∀ {S : Type u_1} [inst : SeminormedGroup S] [IsUltrametricDist S] (x y : S), ‖x * y‖ ≤ max ‖x‖ ‖y‖- 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
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- mul_oneproof · cited by 3,885
- one_mulproof · cited by 2,841
- inv_invproof · cited by 494
- inv_oneproof · cited by 301
- SeminormedGroupstatement and proof · cited by 250
- IsUltrametricDiststatement and proof · cited by 177
- dist_eq_norm_inv_mulproof · cited by 41
- IsUltrametricDist.dist_triangle_maxproof · cited by 8
Cited by3
Results whose statement or proof uses this declaration.
- Finset.Nonempty.norm_prod_le_sup'_normproof · cited by 3
- IsUltrametricDist.nnnorm_mul_le_maxproof · cited by 1
- IsUltrametricDist.exists_norm_multiset_prod_leproof · cited by 0