Theorems · Theorem · group theory
vsub_left_cancel
∀ {G : Type u_1} {P : Type u_2} [inst : AddGroup G] [T : AddTorsor G P] {p₁ p₂ p : P}, p₁ -ᵥ p = p₂ -ᵥ p → p₁ = p₂If the same point subtracted from two points produces equal results, those points are equal.
- Defined in
- Mathlib.Algebra.Torsor.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- AddTorsorstatement and proof · cited by 1,657
- VSub.vsubstatement and proof · cited by 817
- sub_eq_zeroproof · cited by 407
- vsub_eq_zero_iff_eqproof · cited by 45
- vsub_sub_vsub_cancel_rightproof · cited by 39
Cited by6
Results whose statement or proof uses this declaration.
- vsub_left_injectiveproof · cited by 8
- vsub_left_cancel_iffproof · cited by 3
- affineIndependent_set_iff_linearIndependent_vsubproof · cited by 3
- Affine.Simplex.midpoint_faceOppositeCentroid_eulerPointproof · cited by 1
- EuclideanGeometry.Sphere.dist_center_lt_radius_of_sbtwproof · cited by 1
- EuclideanGeometry.Sphere.angle_center_eq_zero_iff_eqproof · cited by 0