Theorems · Theorem · group theory
vsub_vadd
∀ {G : Type u_1} {P : Type u_2} [inst : AddGroup G] [T : AddTorsor G P] (p₁ p₂ : P), (p₁ -ᵥ p₂) +ᵥ p₂ = p₁Adding the result of subtracting from another point produces that point.
- Defined in
- Mathlib.Algebra.Torsor.Defs
- Cited by
- 62 results in Mathlib
- Foundations
- Depth 5 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 · cited by 1,820
- AddTorsorstatement and proof · cited by 1,657
- VSub.vsubstatement · cited by 817
- AddTorsor.vsub_vadd'proof · cited by 1
Cited by63
Results whose statement or proof uses this declaration.
- vsub_add_vsub_cancelproof · cited by 41
- vadd_vsub_assocproof · cited by 40
- vsub_sub_vsub_cancel_rightproof · cited by 39
- AffineMap.lineMap_apply_oneproof · cited by 37
- AffineMap.linearMap_vsubproof · cited by 17
- eq_vadd_iff_vsub_eqproof · cited by 16
- affineCombination_mem_affineSpanproof · cited by 12
- AffineSubspace.ext_of_direction_eqproof · cited by 11
- collinear_pairproof · cited by 8
- Equiv.vaddConstproof · cited by 8
- AffineEquiv.pointReflection_midpoint_leftproof · cited by 5
- AffineEquiv.pointReflection_selfproof · cited by 5