Theorems · Theorem · functional analysis
inner_neg_left
∀ {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
- 33 results in Mathlib
- Foundations
- Depth 159 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.
- InnerProductSpacestatement and proof · cited by 3,523
- one_mulproof · cited by 2,841
- RCLikestatement and proof · cited by 2,829
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- Inner.innerstatement and proof · cited by 1,089
- map_oneproof · cited by 861
- starRingEndproof · cited by 671
- neg_mulproof · cited by 654
- map_negproof · cited by 378
- inner_smul_leftproof · cited by 49
- neg_one_smulproof · cited by 23
Cited by33
Results whose statement or proof uses this declaration.
- inner_neg_rightproof · cited by 41
- inner_sub_leftproof · cited by 24
- EuclideanGeometry.angle_eq_arcsin_of_angle_eq_pi_div_twoproof · cited by 3
- EuclideanGeometry.angle_lt_pi_div_two_of_angle_eq_pi_div_twoproof · cited by 2
- EuclideanGeometry.cos_angle_mul_dist_of_angle_eq_pi_div_twoproof · cited by 2
- EuclideanGeometry.cos_angle_of_angle_eq_pi_div_twoproof · cited by 2
- EuclideanGeometry.sin_angle_mul_dist_of_angle_eq_pi_div_twoproof · cited by 2
- EuclideanGeometry.sin_angle_of_angle_eq_pi_div_twoproof · cited by 2
- EuclideanGeometry.dist_div_cos_angle_of_angle_eq_pi_div_twoproof · cited by 2
- EuclideanGeometry.tan_angle_mul_dist_of_angle_eq_pi_div_twoproof · cited by 2
- EuclideanGeometry.tan_angle_of_angle_eq_pi_div_twoproof · cited by 2
- EuclideanGeometry.dist_div_sin_angle_of_angle_eq_pi_div_twoproof · cited by 2