Theorems · Theorem · group theory
vadd_eq_vadd_iff_neg_add_eq_vsub
∀ {G : Type u_1} {P : Type u_2} [inst : AddGroup G] [T : AddTorsor G P] {v₁ v₂ : G} {p₁ p₂ : P},
v₁ +ᵥ p₁ = v₂ +ᵥ p₂ ↔ -v₁ + v₂ = p₁ -ᵥ p₂- Defined in
- Mathlib.Algebra.Torsor.Defs
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext
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.hVAddstatement and proof · cited by 1,820
- AddTorsorstatement and proof · cited by 1,657
- VSub.vsubstatement and proof · cited by 817
- neg_add_cancel_leftproof · cited by 84
- add_right_injproof · cited by 71
- vadd_vsub_assocproof · cited by 40
- eq_vadd_iff_vsub_eqproof · cited by 16
Cited by1
Results whose statement or proof uses this declaration.
- vadd_eq_vadd_iff_sub_eq_vsubproof · cited by 3