Theorems · Theorem · geometry

EuclideanGeometry.oangle_pointReflection_left

∀ {V : Type u_1} {P : Type u_2} [inst : NormedAddCommGroup V] [inst_1 : InnerProductSpace ℝ V] [inst_2 : MetricSpace P]
  [inst_3 : NormedAddTorsor V P] [hd2 : Fact (Module.finrank ℝ V = 2)] [inst_4 : Module.Oriented ℝ V (Fin 2)]
  {p₁ p₂ p₃ : P},
  p₁ ≠ p₂ →
    p₃ ≠ p₂ →
      EuclideanGeometry.oangle ((AffineEquiv.pointReflection ℝ p₂) p₁) p₂ p₃ =
        EuclideanGeometry.oangle p₁ p₂ p₃ + ↑Real.pi

Defined in: Mathlib.Geometry.Euclidean.Angle.Oriented.Affine
Cited by: 1 results in Mathlib
Foundations: Depth 287 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NormedAddCommGroup InnerProductSpace MetricSpace NormedAddTorsor Fact Module.Oriented

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

DFunLike.coestatement and proof · cited by 62,936
Realstatement and proof · cited by 25,697
NormedAddCommGroupstatement and proof · cited by 15,752
InnerProductSpacestatement and proof · cited by 3,523
Factstatement and proof · cited by 2,726
Real.pistatement and proof · cited by 1,774
Module.finrankstatement and proof · cited by 1,770
MetricSpacestatement and proof · cited by 1,684
NormedAddTorsorstatement and proof · cited by 1,325
Real.Anglestatement and proof · cited by 518
Real.Angle.coestatement and proof · cited by 360
AffineEquivstatement · cited by 191

Cited by1

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EuclideanGeometry.angle_eq_pi_sub_angle_div_two_of_oangle_eq_of_sOppSideproof · cited by 1