Theorems · Theorem · functional analysis
WithLp.prod_sup_edist_ne_top_aux
∀ {α : Type u_2} {β : Type u_3} [inst : PseudoMetricSpace α] [inst_1 : PseudoMetricSpace β] (f g : WithLp ⊤ (α × β)),
max (edist f.fst g.fst) (edist f.snd g.snd) ≠ ⊤An auxiliary lemma used twice in the proof of WithLp.prodPseudoMetricAux below. Not intended
for use outside this file.
- Defined in
- Mathlib.Analysis.Normed.Lp.ProdLp
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 147 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- ENNRealstatement · cited by 9,879
- Top.topstatement and proof · cited by 9,680
- PseudoMetricSpacestatement and proof · cited by 1,550
- EDist.ediststatement · cited by 735
- WithLpstatement and proof · cited by 345
- ne_of_ltproof · cited by 203
- WithLp.sndstatement and proof · cited by 76
- WithLp.fststatement and proof · cited by 76
- PseudoMetricSpace.edist_distproof · cited by 3
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