Theorems · Theorem · functional analysis
inner_neg_right
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : SeminormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
(x y : E), inner 𝕜 x (-y) = -inner 𝕜 x y- Defined in
- Mathlib.Analysis.InnerProductSpace.Basic
- Cited by
- 41 results in Mathlib
- Foundations
- Depth 160 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.
- DFunLike.coeproof · cited by 62,936
- 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
- starRingEndproof · cited by 671
- map_negproof · cited by 378
- inner_conj_symmproof · cited by 48
- inner_neg_leftproof · cited by 33
Cited by41
Results whose statement or proof uses this declaration.
- inner_sub_rightproof · cited by 19
- InnerProductGeometry.angle_neg_rightproof · cited by 7
- norm_sub_sqproof · cited by 5
- Real.fourierInv_eq_fourier_negproof · cited by 4
- MeasureTheory.charFun_eq_fourierIntegral'proof · cited by 3
- inner_vsub_right_eq_zero_symmproof · cited by 2
- ClosedSubmodule.mulI_orthogonal_eq_symplCompproof · cited by 2
- signedDist_vadd_left_swapproof · cited by 2
- real_inner_div_norm_mul_norm_eq_neg_one_iffproof · cited by 2
- ContMDiff.codRestrict_sphereproof · cited by 2
- MeasureTheory.charFun_eq_fourierIntegralproof · cited by 1
- inner_neg_negproof · cited by 1