Theorems · Theorem · group theory
vsub_self
∀ {G : Type u_1} {P : Type u_2} [inst : AddGroup G] [T : AddTorsor G P] (p : P), p -ᵥ p = 0Subtracting a point from itself produces 0.
- Defined in
- Mathlib.Algebra.Torsor.Defs
- Cited by
- 74 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
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.
Cited by74
Results whose statement or proof uses this declaration.
- neg_vsub_eq_vsub_revproof · cited by 87
- vsub_eq_zero_iff_eqproof · cited by 45
- AffineSubspace.self_mem_mk'proof · cited by 10
- vadd_vsub_vadd_cancel_rightproof · cited by 9
- Finset.affineCombination_of_eq_one_of_eq_zeroproof · cited by 8
- EuclideanGeometry.angle_self_leftproof · cited by 8
- signedDist_selfproof · cited by 7
- EuclideanGeometry.oangle_self_rightproof · cited by 7
- Sbtw.angle₁₂₃_eq_piproof · cited by 6
- EuclideanGeometry.inversion_selfproof · cited by 6
- vectorSpan_singletonproof · cited by 6
- AffineMap.lineMap_same_applyproof · cited by 5