Theorems · Theorem · functional analysis
norm_sub_sq
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : SeminormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
(x y : E), ‖x - y‖ ^ 2 = ‖x‖ ^ 2 - 2 * RCLike.re (inner 𝕜 x y) + ‖y‖ ^ 2Expand the square
- Defined in
- Mathlib.Analysis.InnerProductSpace.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 162 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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
- Norm.normstatement and proof · cited by 5,413
- InnerProductSpacestatement and proof · cited by 3,523
- AddMonoidHomstatement · cited by 3,230
- RCLikestatement and proof · cited by 2,829
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- Inner.innerstatement and proof · cited by 1,089
- sub_eq_add_negproof · cited by 1,023
- mul_negproof · cited by 590
- map_negproof · cited by 378
- AddMonoid.toZerostatement · cited by 325
Cited by5
Results whose statement or proof uses this declaration.
- norm_sub_mul_selfproof · cited by 5
- norm_sub_sq_realproof · cited by 3
- Orthonormal.sum_inner_products_leproof · cited by 2
- norm_eq_iInf_iff_real_inner_le_zeroproof · cited by 1
- norm_sub_pow_twoproof · cited by 0