Theorems · Theorem · functional analysis
WithLp.prod_nndist_eq_of_L2
∀ {α : Type u_2} {β : Type u_3} [inst : SeminormedAddCommGroup α] [inst_1 : SeminormedAddCommGroup β]
(x y : WithLp 2 (α × β)), nndist x y = NNReal.sqrt (nndist x.fst y.fst ^ 2 + nndist x.snd y.snd ^ 2)- Defined in
- Mathlib.Analysis.Normed.Lp.ProdLp
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 222 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- ENNRealstatement · cited by 9,879
- NNRealstatement · cited by 4,310
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- Dist.distproof · cited by 1,539
- OrderIsostatement · cited by 874
- WithLpstatement and proof · cited by 345
- NNDist.nndiststatement · cited by 235
- NNReal.eqproof · cited by 201
- NNReal.sqrtstatement · cited by 91
- WithLp.fststatement · cited by 76
- WithLp.sndstatement · cited by 76
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