Theorems · Theorem · group theory
vsub_sub_vsub_cancel_left
∀ {G : Type u_1} {P : Type u_2} [inst : AddCommGroup G] [inst_1 : AddTorsor G P] (p₁ p₂ p₃ : P),
p₃ -ᵥ p₂ - (p₃ -ᵥ p₁) = p₁ -ᵥ p₂Cancellation subtracting the results of two subtractions.
- Defined in
- Mathlib.Algebra.Torsor.Basic
- Cited by
- 18 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses no axioms
- Assumes
- AddCommGroupAddTorsor
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- AddTorsorstatement and proof · cited by 1,657
- add_commproof · cited by 1,535
- sub_eq_add_negproof · cited by 1,023
- VSub.vsubstatement and proof · cited by 817
- neg_vsub_eq_vsub_revproof · cited by 87
- vsub_add_vsub_cancelproof · cited by 41
Cited by18
Results whose statement or proof uses this declaration.
- vectorSpan_eq_span_vsub_set_leftproof · cited by 4
- EuclideanGeometry.mul_dist_eq_abs_sub_sq_distproof · cited by 3
- EuclideanGeometry.oangle_swap₁₂_signproof · cited by 2
- EuclideanGeometry.abs_oangle_right_toReal_lt_pi_div_two_of_dist_eqproof · cited by 2
- EuclideanGeometry.oangle_eq_oangle_of_dist_eqproof · cited by 2
- Finset.weightedVSubOfPoint_vadd_eq_of_sum_eq_oneproof · cited by 2
- vsub_vadd_commproof · cited by 2
- Affine.Simplex.faceOppositeCentroid_mem_ninePointCircleproof · cited by 2
- dist_vsub_cancel_leftproof · cited by 1
- EuclideanGeometry.dist_eq_iff_eq_smul_rotation_pi_div_two_vadd_midpointproof · cited by 1
- EuclideanGeometry.dist_eq_of_angle_eq_angle_of_angle_ne_piproof · cited by 1
- Finset.weightedVSubOfPoint_eq_of_sum_eq_zeroproof · cited by 1