Theorems · Theorem · functional analysis
inner_self_ofReal_norm
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : SeminormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
(x : E), ↑‖inner 𝕜 x x‖ = inner 𝕜 x x- Defined in
- Mathlib.Analysis.InnerProductSpace.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 169 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realproof · cited by 25,697
- Norm.normstatement · cited by 5,413
- InnerProductSpacestatement and proof · cited by 3,523
- RCLikestatement and proof · cited by 2,829
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- Inner.innerstatement and proof · cited by 1,089
- RCLike.ofRealstatement and proof · cited by 350
- inner_self_ofReal_reproof · cited by 3
- inner_self_re_eq_normproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- real_inner_self_absproof · cited by 0