Theorems · Theorem · functional analysis
real_inner_comm
∀ {F : Type u_3} [inst : SeminormedAddCommGroup F] [inst_1 : InnerProductSpace ℝ F] (x y : F), inner ℝ y x = inner ℝ x y- Defined in
- Mathlib.Analysis.InnerProductSpace.Basic
- Cited by
- 57 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.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- InnerProductSpacestatement and proof · cited by 3,523
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- Inner.innerstatement · cited by 1,089
- inner_conj_symmproof · cited by 48
Cited by57
Results whose statement or proof uses this declaration.
- InnerProductGeometry.angle_commproof · cited by 14
- Orientation.inner_rev_eq_zero_of_oangle_eq_pi_div_twoproof · cited by 12
- MeasureTheory.charFun_eq_charFunDual_toDualMapproof · cited by 6
- hasStrictFDerivAt_norm_sqproof · cited by 6
- flip_innerₗproof · cited by 4
- OrthonormalBasis.sum_sq_inner_leftproof · cited by 3
- InnerProductSpace.canonicalCovariantTensor_eq_sumproof · cited by 3
- 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