Theorems · Theorem · group theory
neg_vsub_eq_vsub_rev
∀ {G : Type u_1} {P : Type u_2} [inst : AddGroup G] [T : AddTorsor G P] (p₁ p₂ : P), -(p₁ -ᵥ p₂) = p₂ -ᵥ p₁Subtracting two points in the reverse order produces the negation of subtracting them.
- Defined in
- Mathlib.Algebra.Torsor.Defs
- Cited by
- 87 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses no axioms
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.
- AddGroupstatement and proof · cited by 4,410
- HVAdd.hVAddproof · cited by 1,820
- AddTorsorstatement and proof · cited by 1,657
- VSub.vsubstatement · cited by 817
- vsub_selfproof · cited by 74
- vsub_add_vsub_cancelproof · cited by 41
- neg_eq_of_add_eq_zero_rightproof · cited by 9
- vadd_right_cancelproof · cited by 6
Cited by87
Results whose statement or proof uses this declaration.
- vsub_vadd_eq_vsub_subproof · cited by 32
- vsub_sub_vsub_cancel_leftproof · cited by 18
- EuclideanGeometry.angle_add_angle_add_angle_eq_piproof · cited by 10
- slope_commproof · cited by 9
- EuclideanGeometry.angle_eq_pi_iff_sbtwproof · cited by 6
- EuclideanGeometry.reflection_apply'proof · cited by 6
- AffineSubspace.wOppSide_commproof · cited by 6
- Affine.Simplex.centroid_vsub_point_eq_smul_vsubproof · cited by 5
- Affine.Simplex.point_vsub_centroid_eq_smul_vsubproof · cited by 4
- Wbtw.wOppSide₁₃proof · cited by 4
- vsub_midpointproof · cited by 4
- EuclideanGeometry.coe_orthogonalProjection_eq_iff_memproof · cited by 4