Theorems · Theorem · group theory
add_neg_cancel_right
∀ {G : Type u_1} [inst : AddGroup G] (a b : G), a + b + -b = a- Defined in
- Mathlib.Algebra.Group.Defs
- Cited by
- 65 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses no axioms
- Assumes
- AddGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- add_assocproof · cited by 746
- add_neg_cancelproof · cited by 213
Cited by65
Results whose statement or proof uses this declaration.
- add_sub_cancel_rightproof · cited by 187
- Set.image_add_rightproof · cited by 37
- add_neg_eq_iff_eq_addproof · cited by 12
- eq_add_neg_iff_add_eqproof · cited by 12
- add_mem_cancel_rightproof · cited by 10
- IsCoprime.add_mul_left_leftproof · cited by 6
- IsRelPrime.add_mul_left_leftproof · cited by 5
- mem_rightAddCoset_iffproof · cited by 4
- LiouvilleWith.add_rat_iffproof · cited by 4
- neg_add_cancel_comm_assocproof · cited by 4
- AddSubgroup.isComplement_iff_existsUnique_add_neg_memproof · cited by 3
- mapClusterPt_self_zsmul_atTop_nsmulproof · cited by 3