Mathlib Map

Theorems · Theorem · geometry

Orientation.oangle_rev

∀ {V : Type u_1} [inst : NormedAddCommGroup V] [inst_1 : InnerProductSpace ℝ V] [inst_2 : Fact (Module.finrank ℝ V = 2)]
  (o : Orientation ℝ V (Fin 2)) (x y : V), o.oangle y x = -o.oangle x y

Swapping the two vectors passed to oangle negates the angle.

Defined in
Mathlib.Geometry.Euclidean.Angle.Oriented.Basic
Cited by
42 results in Mathlib
Foundations
Depth 254 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NormedAddCommGroupInnerProductSpaceFact

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Orientation.oangle_sign_sub_right_swap · cited by 13Orientation.oangle_sign_s…EuclideanGeometry.oangle_rev · cited by 8EuclideanGeometry.oangle_…Orientation.oangle_add_right_smul_rotation_pi_div_two · cited by 4Orientation.oangle_add_ri…Orientation.oangle_sign_add_smul_left · cited by 3Orientation.oangle_sign_a…Orientation.angle_eq_iff_oangle_eq_neg_of_sign_eq_neg · cited by 2Orientation.angle_eq_iff_…Orientation.oangle_add_left_smul_rotation_pi_div_two · cited by 2Orientation.oangle_add_le…Orientation.oangle_add_oangle_rev · cited by 2Orientation.oangle_add_oa…Orientation.oangle_eq_pi_iff_oangle_rev_eq_pi · cited by 2Orientation.oangle_eq_pi_…Orientation.oangle_sign_sub_left_swap · cited by 2Orientation.oangle_sign_s…Orientation.norm_eq_of_two_zsmul_oangle_sub_eq · cited by 1Orientation.norm_eq_of_tw…Orientation.oangle_eq_neg_of_angle_eq_of_sign_eq_neg · cited by 1Orientation.oangle_eq_neg…Orientation.oangle_eq_zero_iff_oangle_rev_eq_zero · cited by 1Orientation.oangle_eq_zer…Orientation.oangle_sign_smul_add_smul_left · cited by 1Orientation.oangle_sign_s…Orientation.oangle_sub_left_eq_arccos_of_oangle_eq_pi_div_two · cited by 0Orientation.oangle_sub_le…Orientation.oangle_sub_left_eq_arcsin_of_oangle_eq_pi_div_two · cited by 0Orientation.oangle_sub_le…DFunLike.coe · cited by 62936DFunLike.coeReal · cited by 25697RealNormedAddCommGroup · cited by 15752NormedAddCommGroupInnerProductSpace · cited by 3523InnerProductSpaceFact · cited by 2726FactModule.finrank · cited by 1770Module.finrankReal.Angle · cited by 518Real.AngleReal.Angle.coe · cited by 360Angle.coeOrientation · cited by 360OrientationComplex.arg · cited by 220Complex.argOrientation.oangle · cited by 205Orientation.oangleOrientation.kahler · cited by 39Orientation.kahlerComplex.arg_conj_coe_angle · cited by 2Complex.arg_conj_coe_angleOrientation.kahler_swap · cited by 1Orientation.kahler_swapOrientation.oangle_revCITED BYCITES

Cites14

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

Cited by42

Results whose statement or proof uses this declaration.