Theorems · Theorem · group theory
vsub_ne_zero
∀ {G : Type u_1} {P : Type u_2} [inst : AddGroup G] [T : AddTorsor G P] {p q : P}, p -ᵥ q ≠ 0 ↔ p ≠ q- Defined in
- Mathlib.Algebra.Torsor.Defs
- Cited by
- 39 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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 · cited by 817
- vsub_eq_zero_iff_eqproof · cited by 45
Cited by39
Results whose statement or proof uses this declaration.
- EuclideanGeometry.angle_self_of_neproof · cited by 6
- Sbtw.angle₁₂₃_eq_piproof · cited by 6
- EuclideanGeometry.angle_eq_pi_iff_sbtwproof · cited by 6
- Wbtw.angle₂₁₃_eq_zero_of_neproof · cited by 5
- EuclideanGeometry.right_ne_of_oangle_ne_zeroproof · cited by 4
- EuclideanGeometry.left_ne_of_oangle_ne_zeroproof · cited by 4
- EuclideanGeometry.oangle_addproof · cited by 4
- EuclideanGeometry.inner_pos_or_eq_of_dist_le_radiusproof · cited by 3
- EuclideanGeometry.dist_inversion_inversionproof · cited by 3
- EuclideanGeometry.angle_eq_abs_oangle_toRealproof · cited by 3
- EuclideanGeometry.angle_eq_arcsin_of_angle_eq_pi_div_twoproof · cited by 3
- EuclideanGeometry.angle_eq_zero_iff_ne_and_wbtwproof · cited by 3