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Theorems · Theorem · functional analysis

WithLp.nndist_fst_le

∀ {p : ENNReal} {α : Type u_2} {β : Type u_3} [hp : Fact (1 ≤ p)] [inst : PseudoMetricSpace α]
  [inst_1 : PseudoMetricSpace β] (x y : WithLp p (α × β)), nndist x.fst y.fst ≤ nndist x y
Defined in
Mathlib.Analysis.Normed.Lp.ProdLp
Cited by
2 results in Mathlib
Foundations
Depth 219 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FactPseudoMetricSpacePseudoMetricSpace
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

WithLp.dist_fst_le · cited by 1WithLp.dist_fst_leWithLp.nnnorm_fst_le · cited by 0WithLp.nnnorm_fst_leENNReal · cited by 9879ENNRealNNReal · cited by 4310NNRealFact · cited by 2726FactPseudoMetricSpace · cited by 1550PseudoMetricSpaceWithLp · cited by 345WithLpNNDist.nndist · cited by 235NNDist.nndistWithLp.fst · cited by 76WithLp.fstWithLp.edist_fst_le · cited by 2WithLp.edist_fst_leWithLp.nndist_fst_leCITED BYCITES

Cites8

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Cited by2

Results whose statement or proof uses this declaration.