InnerProductGeometry.angle_sub_eq_angle_sub_rev_of_norm_eq
∀ {V : Type u_1} [inst : NormedAddCommGroup V] [inst_1 : InnerProductSpace ℝ V] {x y : V},
‖x‖ = ‖y‖ → InnerProductGeometry.angle x (x - y) = InnerProductGeometry.angle y (y - x)Pons asinorum, vector angle form.
- Defined in
- Mathlib.Geometry.Euclidean.Triangle
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 191 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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.normstatement and proof · cited by 5,413
- InnerProductSpacestatement and proof · cited by 3,523
- Inner.innerproof · cited by 1,089
- Real.cosproof · cited by 424
- neg_subproof · cited by 272
- norm_negproof · cited by 190
- InnerProductGeometry.anglestatement and proof · cited by 170
- real_inner_commproof · cited by 57
- inner_sub_rightproof · cited by 19
- real_inner_self_eq_norm_mul_normproof · cited by 17
Cited by1
Results whose statement or proof uses this declaration.
- EuclideanGeometry.angle_eq_angle_of_dist_eqproof · cited by 0