Theorems · Theorem · functional analysis
nnnorm_add_le
∀ {E : Type u_5} [inst : SeminormedAddGroup E] (a b : E), ‖a + b‖₊ ≤ ‖a‖₊ + ‖b‖₊- Defined in
- Mathlib.Analysis.Normed.Group.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 114 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.
Cites5
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
- SeminormedAddGroupstatement and proof · cited by 331
- NNReal.coe_le_coeproof · cited by 73
- norm_add_leproof · cited by 68
Cited by3
Results whose statement or proof uses this declaration.
- SpectrumRestricts.nnreal_addproof · cited by 2
- MeasureTheory.Submartingale.upcrossings_ae_lt_top'proof · cited by 1
- FormalMultilinearSeries.changeOrigin_evalproof · cited by 1