Theorems · Theorem · functional analysis
WithLp.prod_dist_eq_of_L2
∀ {α : Type u_2} {β : Type u_3} [inst : SeminormedAddCommGroup α] [inst_1 : SeminormedAddCommGroup β]
(x y : WithLp 2 (α × β)), dist x y = √(dist x.fst y.fst ^ 2 + dist x.snd y.snd ^ 2)- Defined in
- Mathlib.Analysis.Normed.Lp.ProdLp
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 221 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- ENNRealstatement · cited by 9,879
- Norm.normproof · cited by 5,413
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- Dist.diststatement · cited by 1,539
- Real.sqrtstatement and proof · cited by 545
- WithLpstatement and proof · cited by 345
- dist_eq_normproof · cited by 182
- WithLp.fststatement and proof · cited by 76
- WithLp.sndstatement and proof · cited by 76
- WithLp.prod_norm_eq_of_L2proof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- WithLp.prod_nndist_eq_of_L2proof · cited by 0