Theorems · Theorem · group theory
vsub_add_vsub_cancel
∀ {G : Type u_1} {P : Type u_2} [inst : AddGroup G] [T : AddTorsor G P] (p₁ p₂ p₃ : P), p₁ -ᵥ p₂ + (p₂ -ᵥ p₃) = p₁ -ᵥ p₃Cancellation adding the results of two subtractions.
- Defined in
- Mathlib.Algebra.Torsor.Defs
- Cited by
- 41 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
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.
- AddGroupstatement and proof · cited by 4,410
- HVAdd.hVAddproof · cited by 1,820
- AddTorsorstatement and proof · cited by 1,657
- VSub.vsubstatement and proof · cited by 817
- vsub_vaddproof · cited by 62
- AddSemigroupAction.add_vaddproof · cited by 43
- vadd_right_cancelproof · cited by 6
Cited by41
Results whose statement or proof uses this declaration.
- neg_vsub_eq_vsub_revproof · cited by 87
- vsub_vadd_eq_vsub_subproof · cited by 32
- vsub_sub_vsub_cancel_leftproof · cited by 18
- AffineSubspace.shift_eqproof · cited by 3
- EuclideanGeometry.mul_dist_eq_abs_sub_sq_distproof · cited by 3
- EuclideanGeometry.angle_eq_arcsin_of_angle_eq_pi_div_twoproof · cited by 3
- AffineSubspace.direction_supproof · cited by 2
- EuclideanGeometry.angle_lt_pi_div_two_of_angle_eq_pi_div_twoproof · cited by 2
- Wbtw.trans_expand_leftproof · cited by 2
- Finset.weightedVSubOfPoint_vadd_eq_of_sum_eq_oneproof · cited by 2