Theorems · Theorem · functional analysis
InnerProductSpaceable.inner_.norm_sq
∀ {𝕜 : Type u_1} [inst : RCLike 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace 𝕜 E] (x : E),
‖x‖ ^ 2 = RCLike.re (inner_✝ 𝕜 x x)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 165 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites29
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- Norm.normstatement and proof · cited by 5,413
- Algebra.algebraMapproof · cited by 4,706
- AddMonoidHomstatement · cited by 3,230
- RCLikestatement and proof · cited by 2,829
- zero_addproof · cited by 2,366
- Nat.cast_zeroproof · cited by 1,870
- sub_selfproof · cited by 996
- map_addproof · cited by 964
Cited by2
Results whose statement or proof uses this declaration.
- InnerProductSpace.ofNormproof · cited by 0
- nonempty_innerProductSpaceproof · cited by 0