Theorems · Definition · geometry
EuclideanGeometry.o
{R : Type u_3} →
{inst : CommSemiring R} →
{inst_1 : PartialOrder R} →
{inst_2 : IsStrictOrderedRing R} →
{M : Type u_4} →
{inst_3 : AddCommMonoid M} →
{inst_4 : Module R M} → {ι : Type u_5} → [self : Module.Oriented R M ι] → Orientation R M ιA fixed choice of positive orientation of Euclidean space ℝ²
- Cited by
- 48 results in Mathlib
- Foundations
- Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Module.Oriented
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement · cited by 20,661
- AddCommMonoidstatement · cited by 12,281
- CommSemiringstatement · cited by 10,911
- PartialOrderstatement · cited by 6,410
- IsStrictOrderedRingstatement · cited by 2,490
- Orientationstatement · cited by 360
- Module.Orientedstatement · cited by 190
- Module.Oriented.positiveOrientationproof · cited by 15
Cited by49
Results whose statement or proof uses this declaration.
- EuclideanGeometry.oangleproof · cited by 188
- EuclideanGeometry.oangle_eq_angle_of_sign_eq_oneproof · cited by 24
- EuclideanGeometry.angle_eq_pi_div_two_of_oangle_eq_pi_div_twoproof · cited by 13
- EuclideanGeometry.oangle_revproof · cited by 8
- EuclideanGeometry.oangle_self_rightproof · cited by 7
- EuclideanGeometry.oangle_self_leftproof · cited by 5
- EuclideanGeometry.right_ne_of_oangle_ne_zeroproof · cited by 4
- EuclideanGeometry.left_ne_of_oangle_ne_zeroproof · cited by 4
- EuclideanGeometry.left_ne_right_of_oangle_ne_zeroproof · cited by 4
- EuclideanGeometry.oangle_addproof · cited by 4
- EuclideanGeometry.oangle_ne_zero_and_ne_pi_iff_affineIndependentproof · cited by 4
- EuclideanGeometry.angle_eq_abs_oangle_toRealproof · cited by 3