Theorems · Theorem · group theory
vadd_right_cancel
∀ {G : Type u_1} {P : Type u_2} [inst : AddGroup G] [T : AddTorsor G P] {g₁ g₂ : G} (p : P), g₁ +ᵥ p = g₂ +ᵥ p → g₁ = g₂If the same point added to two group elements produces equal results, those group elements are equal.
- Defined in
- Mathlib.Algebra.Torsor.Defs
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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.hVAddstatement and proof · cited by 1,820
- AddTorsorstatement and proof · cited by 1,657
- VSub.vsubproof · cited by 817
- vadd_vsubproof · cited by 58
Cited by6
Results whose statement or proof uses this declaration.
- neg_vsub_eq_vsub_revproof · cited by 87
- vsub_add_vsub_cancelproof · cited by 41
- vadd_vsub_assocproof · cited by 40
- vadd_right_cancel_iffproof · cited by 4
- affineIndependent_set_iff_linearIndependent_vsubproof · cited by 3
- vadd_right_injectiveproof · cited by 2