Theorems · Theorem · functional analysis
abs_real_inner_le_norm
∀ {F : Type u_3} [inst : SeminormedAddCommGroup F] [inst_1 : InnerProductSpace ℝ F] (x y : F), |inner ℝ x y| ≤ ‖x‖ * ‖y‖Cauchy–Schwarz inequality with norm
- Defined in
- Mathlib.Analysis.InnerProductSpace.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 171 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Norm.normstatement · cited by 5,413
- InnerProductSpacestatement and proof · cited by 3,523
- LE.le.transproof · cited by 3,151
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- absstatement · cited by 1,814
- Inner.innerstatement and proof · cited by 1,089
- Eq.geproof · cited by 375
- Real.norm_eq_absproof · cited by 88
- norm_inner_le_normproof · cited by 14
Cited by7
Results whose statement or proof uses this declaration.
- abs_real_inner_div_norm_mul_norm_le_oneproof · cited by 4
- real_inner_le_normproof · cited by 4
- Affine.Simplex.abs_inner_vsub_altitudeFoot_lt_mulproof · cited by 2
- Orientation.abs_volumeForm_apply_leproof · cited by 2
- neg_one_le_real_inner_of_norm_eq_oneproof · cited by 1
- abs_signedDist_le_distproof · cited by 1
- TemperedDistribution.MemSobolev.lineDerivOpproof · cited by 0