Theorems · Theorem · functional analysis
inner_sub_right
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : SeminormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
(x y z : E), inner 𝕜 x (y - z) = inner 𝕜 x y - inner 𝕜 x z- Defined in
- Mathlib.Analysis.InnerProductSpace.Basic
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 161 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- 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
- inner_neg_rightproof · cited by 41
- inner_add_rightproof · cited by 27
Cited by19
Results whose statement or proof uses this declaration.
- ext_inner_leftproof · cited by 11
- InnerProductSpace.gramSchmidt_orthogonalproof · cited by 6
- inner_sub_sub_selfproof · cited by 3
- MeasureTheory.integral_condExpL2_eqproof · cited by 3
- InnerProductGeometry.sin_angle_mul_norm_eq_sin_angle_mul_normproof · cited by 2
- inner_map_polarizationproof · cited by 2
- Dense.eq_of_inner_rightproof · cited by 2
- real_inner_add_sub_eq_zero_iffproof · cited by 2
- inner_map_polarization'proof · cited by 1
- eq_of_norm_le_re_inner_eq_norm_sqproof · cited by 1
- InnerProductGeometry.angle_sub_eq_angle_sub_rev_of_norm_eqproof · cited by 1