InnerProductGeometry.angle_eq_angle_add_add_angle_add
∀ {V : Type u_1} [inst : NormedAddCommGroup V] [inst_1 : InnerProductSpace ℝ V] (x : V) {y : V},
y ≠ 0 → InnerProductGeometry.angle x y = InnerProductGeometry.angle x (x + y) + InnerProductGeometry.angle y (x + y)In a parallelogram, the two parts of the inner angle add to the inner angle, vector angle form.
- Defined in
- Mathlib.Geometry.Euclidean.Triangle
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 198 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites45
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
- InnerProductSpacestatement and proof · cited by 3,523
- add_zeroproof · cited by 2,707
- Nat.cast_oneproof · cited by 2,501
- zero_addproof · cited by 2,366
- le_reflproof · cited by 2,061
- Nat.cast_zeroproof · cited by 1,870
- Real.piproof · cited by 1,774
- add_commproof · cited by 1,535
- one_smulproof · cited by 1,374
- le_of_ltproof · cited by 1,175
Cited by2
Results whose statement or proof uses this declaration.
- InnerProductGeometry.angle_add_angle_sub_add_angle_sub_eq_piproof · cited by 1
- InnerProductGeometry.angle_eq_angle_add_add_angle_add_of_mem_spanproof · cited by 1