Theorems · Theorem · geometry

EuclideanGeometry.oangle_self_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 : P), EuclideanGeometry.oangle p₁ p₁ p₂ = 0

The angle ∡AAB at a point.

Defined in: Mathlib.Geometry.Euclidean.Angle.Oriented.Affine
Cited by: 5 results in Mathlib
Foundations: Depth 253 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NormedAddCommGroup InnerProductSpace MetricSpace NormedAddTorsor Fact Module.Oriented

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Cites15

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
Factstatement and proof · cited by 2,726
Module.finrankstatement and proof · cited by 1,770
MetricSpacestatement and proof · cited by 1,684
NormedAddTorsorstatement and proof · cited by 1,325
VSub.vsubproof · cited by 817
Real.Anglestatement · cited by 518
Module.Orientedstatement and proof · cited by 190
EuclideanGeometry.oanglestatement · cited by 188
vsub_selfproof · cited by 74

Cited by5

Results whose statement or proof uses this declaration.

Wbtw.oangle₂₁₃_eq_zeroproof · cited by 3
EuclideanGeometry.abs_oangle_toReal_lt_pi_div_two_of_angle_eq_pi_div_twoproof · cited by 2
EuclideanGeometry.two_zsmul_oangle_eq_of_dist_orthogonalProjection_line_eqproof · cited by 1
EuclideanGeometry.oangle_midpoint_leftproof · cited by 1
EuclideanGeometry.oangle_eq_zero_iff_wbtwproof · cited by 0