Theorems · Theorem · functional analysis
WithLp.prod_norm_eq_of_L2
∀ {α : Type u_2} {β : Type u_3} [inst : SeminormedAddCommGroup α] [inst_1 : SeminormedAddCommGroup β]
(x : WithLp 2 (α × β)), ‖x‖ = √(‖x.fst‖ ^ 2 + ‖x.snd‖ ^ 2)- Defined in
- Mathlib.Analysis.Normed.Lp.ProdLp
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 201 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 and proof · cited by 25,697
- ENNRealstatement · cited by 9,879
- Norm.normstatement and proof · cited by 5,413
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- Nat.cast_oneproof · cited by 2,501
- Real.sqrtstatement and proof · cited by 545
- WithLpstatement and proof · cited by 345
- WithLp.fststatement and proof · cited by 76
- WithLp.sndstatement and proof · cited by 76
- Real.sqrt_eq_rpowproof · cited by 25
- WithLp.prod_norm_eq_of_natproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- WithLp.prod_dist_eq_of_L2proof · cited by 1
- WithLp.prod_nnnorm_eq_of_L2proof · cited by 1