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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 ι

A fixed choice of positive orientation of Euclidean space ℝ²

Defined in
Mathlib.Geometry.Euclidean.Angle.Oriented.Affine
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.

EuclideanGeometry.oangle · cited by 188EuclideanGeometry.oangleEuclideanGeometry.oangle_eq_angle_of_sign_eq_one · cited by 24EuclideanGeometry.oangle_…EuclideanGeometry.angle_eq_pi_div_two_of_oangle_eq_pi_div_two · cited by 13EuclideanGeometry.angle_e…EuclideanGeometry.oangle_rev · cited by 8EuclideanGeometry.oangle_…EuclideanGeometry.oangle_self_right · cited by 7EuclideanGeometry.oangle_…EuclideanGeometry.oangle_self_left · cited by 5EuclideanGeometry.oangle_…EuclideanGeometry.right_ne_of_oangle_ne_zero · cited by 4EuclideanGeometry.right_n…EuclideanGeometry.left_ne_of_oangle_ne_zero · cited by 4EuclideanGeometry.left_ne…EuclideanGeometry.left_ne_right_of_oangle_ne_zero · cited by 4EuclideanGeometry.left_ne…EuclideanGeometry.oangle_add · cited by 4EuclideanGeometry.oangle_…EuclideanGeometry.oangle_ne_zero_and_ne_pi_iff_affineIndependent · cited by 4EuclideanGeometry.oangle_…EuclideanGeometry.angle_eq_abs_oangle_toReal · cited by 3EuclideanGeometry.angle_e…EuclideanGeometry.oangle_swap₁₂_sign · cited by 2EuclideanGeometry.oangle_…Affine.Triangle.circumsphere_eq_circumsphere_of_eq_of_eq_of_two_zsmul_oangle_eq · cited by 2Triangle.circumsphere_eq_…EuclideanGeometry.continuousAt_oangle · cited by 2EuclideanGeometry.continu…Module · cited by 20661ModuleAddCommMonoid · cited by 12281AddCommMonoidCommSemiring · cited by 10911CommSemiringPartialOrder · cited by 6410PartialOrderIsStrictOrderedRing · cited by 2490IsStrictOrderedRingOrientation · cited by 360OrientationModule.Oriented · cited by 190Module.OrientedModule.Oriented.positiveOrientation · cited by 15Oriented.positiveOrientat…EuclideanGeometry.oCITED BYCITES

Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by49

Results whose statement or proof uses this declaration.