Theorems · Theorem · group theory
vsub_vadd_comm
∀ {G : Type u_1} {P : Type u_2} [inst : AddCommGroup G] [inst_1 : AddTorsor G P] (p₁ p₂ p₃ : P),
(p₁ -ᵥ p₂) +ᵥ p₃ = (p₃ -ᵥ p₂) +ᵥ p₁- Defined in
- Mathlib.Algebra.Torsor.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext
- Assumes
- AddCommGroupAddTorsor
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddCommGroupstatement and proof · cited by 12,871
- HVAdd.hVAddstatement and proof · cited by 1,820
- AddTorsorstatement and proof · cited by 1,657
- VSub.vsubstatement and proof · cited by 817
- vsub_selfproof · cited by 74
- vsub_eq_zero_iff_eqproof · cited by 45
- vsub_add_vsub_cancelproof · cited by 41
- vadd_vsub_assocproof · cited by 40
- vsub_vadd_eq_vsub_subproof · cited by 32
- vsub_sub_vsub_cancel_leftproof · cited by 18
Cited by2
Results whose statement or proof uses this declaration.
- vsub_sub_vsub_commproof · cited by 1
- AffineSubspace.shift_eq_map_homothetyproof · cited by 0