InnerProductGeometry.angle_smul_smul
∀ {V : Type u_1} [inst : NormedAddCommGroup V] [inst_1 : InnerProductSpace ℝ V] {c : ℝ},
c ≠ 0 → ∀ (x y : V), InnerProductGeometry.angle (c • x) (c • y) = InnerProductGeometry.angle x y- Cited by
- 1 results in Mathlib
- Foundations
- Depth 190 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
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
- NormedAddCommGroupstatement and proof · cited by 15,752
- Norm.normproof · cited by 5,413
- InnerProductSpacestatement and proof · cited by 3,523
- absproof · cited by 1,814
- mul_assocproof · cited by 1,667
- Inner.innerproof · cited by 1,089
- norm_smulproof · cited by 242
- mul_ne_zeroproof · cited by 178
- InnerProductGeometry.anglestatement and proof · cited by 170
- Real.arccosproof · cited by 90
- Real.norm_eq_absproof · cited by 88
Cited by1
Results whose statement or proof uses this declaration.
- InnerProductGeometry.IsConformalMap.preserves_angleproof · cited by 1