Theorems · Theorem · functional analysis
IsUltrametricDist.nnnorm_add_one_le_max_nnnorm_one
∀ {R : Type u_1} [inst : SeminormedRing R] [NormOneClass R] [IsUltrametricDist R] (x : R), ‖x + 1‖₊ ≤ max ‖x‖₊ 1- Defined in
- Mathlib.Analysis.Normed.Ring.Ultra
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 114 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NNRealstatement · cited by 4,310
- NNNorm.nnnormstatement · cited by 952
- SeminormedRingstatement and proof · cited by 446
- IsUltrametricDiststatement and proof · cited by 177
- NormOneClassstatement and proof · cited by 136
- IsUltrametricDist.norm_add_one_le_max_norm_oneproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- IsUltrametricDist.nnnorm_natCast_le_oneproof · cited by 2