Orientation.oangle.congr_simp
∀ {V : Type u_1} [inst : NormedAddCommGroup V] [inst_1 : InnerProductSpace ℝ V] [inst_2 : Fact (Module.finrank ℝ V = 2)]
(o o_1 : Orientation ℝ V (Fin 2)),
o = o_1 → ∀ (x x_1 : V), x = x_1 → ∀ (y y_1 : V), y = y_1 → o.oangle x y = o_1.oangle x_1 y_1- Cited by
- 41 results in Mathlib
- Foundations
- Depth 252 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- 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
- Real.Anglestatement · cited by 518
- Orientationstatement and proof · cited by 360
- Orientation.oanglestatement and proof · cited by 205
Cited by41
Results whose statement or proof uses this declaration.
- Orientation.oangle_eq_angle_of_sign_eq_oneproof · cited by 25
- EuclideanGeometry.oangle_self_rightproof · cited by 7
- Orientation.oangle_sign_smul_add_rightproof · cited by 6
- EuclideanGeometry.oangle_self_leftproof · cited by 5
- Orientation.oangle_add_right_smul_rotation_pi_div_twoproof · cited by 4
- Orientation.oangle_eq_of_angle_eq_of_sign_eqproof · cited by 3
- Orientation.oangle_eq_pi_iff_sameRay_negproof · cited by 3
- Orientation.eq_zero_or_oangle_eq_iff_inner_eq_zeroproof · cited by 3
- Orientation.oangle_eq_pi_sub_two_zsmul_oangle_sub_of_norm_eqproof · cited by 3
- Orientation.oangle_sign_add_smul_leftproof · cited by 3
- Orientation.oangle_add_left_smul_rotation_pi_div_twoproof · cited by 2
- Orientation.oangle_eq_pi_iff_angle_eq_piproof · cited by 2