Theorems · Theorem · group theory
vsub_sub_vsub_cancel_right
∀ {G : Type u_1} {P : Type u_2} [inst : AddGroup G] [T : AddTorsor G P] (p₁ p₂ p₃ : P), p₁ -ᵥ p₃ - (p₂ -ᵥ p₃) = p₁ -ᵥ p₂Cancellation subtracting the results of two subtractions.
- Defined in
- Mathlib.Algebra.Torsor.Defs
- Cited by
- 39 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.
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
- AddTorsorstatement and proof · cited by 1,657
- VSub.vsubstatement and proof · cited by 817
- vsub_vaddproof · cited by 62
- vsub_vadd_eq_vsub_subproof · cited by 32
Cited by39
Results whose statement or proof uses this declaration.
- AffineSubspace.direction_mk'proof · cited by 15
- EuclideanGeometry.angle_add_angle_add_angle_eq_piproof · cited by 10
- vectorSpan_eq_span_vsub_set_rightproof · cited by 7
- vsub_left_cancelproof · cited by 6
- AffineSubspace.wSameSide_iff_exists_leftproof · cited by 5
- AffineSubspace.wOppSide_iff_exists_leftproof · cited by 5
- Affine.Simplex.point_vsub_centroid_eq_smul_vsubproof · cited by 4
- Finset.sum_smul_vsub_eq_weightedVSubOfPoint_subproof · cited by 4
- EuclideanGeometry.inner_pos_or_eq_of_dist_le_radiusproof · cited by 3
- Wbtw.trans_expand_leftproof · cited by 2
- EuclideanGeometry.inner_weightedVSubproof · cited by 2
- midpoint_vsubproof · cited by 2