Theorems · Theorem · group theory
vadd_vsub_vadd_cancel_right
∀ {G : Type u_1} {P : Type u_2} [inst : AddGroup G] [T : AddTorsor G P] (v₁ v₂ : G) (p : P),
(v₁ +ᵥ p) -ᵥ (v₂ +ᵥ p) = v₁ - v₂- Defined in
- Mathlib.Algebra.Torsor.Defs
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 14 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
- add_zeroproof · cited by 2,707
- HVAdd.hVAddstatement and proof · cited by 1,820
- AddTorsorstatement and proof · cited by 1,657
- VSub.vsubstatement · cited by 817
- vsub_selfproof · cited by 74
- vadd_vsub_assocproof · cited by 40
- vsub_vadd_eq_vsub_subproof · cited by 32
Cited by9
Results whose statement or proof uses this declaration.
- dist_lineMap_lineMapproof · cited by 5
- dist_vadd_cancel_rightproof · cited by 4
- AffineMap.lineMap_eq_lineMap_iffproof · cited by 3
- Finset.sum_smul_vsub_eq_affineCombination_vsubproof · cited by 2
- Finset.affineCombination_sdiff_subproof · cited by 1
- dist_sq_lineMap_lineMap_of_inner_eq_zeroproof · cited by 1
- StarConvex.smul_vadd_mem_of_isClosed_of_mem_asymptoticConeproof · cited by 1
- AffineSubspace.euclideanHausdorffMeasure_eq_lintegralproof · cited by 1
- slope_vadd_constproof · cited by 0