Theorems · Theorem · group theory
add_neg_cancel_left
∀ {G : Type u_1} [inst : AddGroup G] (a b : G), a + (-a + b) = b- Defined in
- Mathlib.Algebra.Group.Defs
- Cited by
- 76 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
- zero_addproof · cited by 2,366
- add_assocproof · cited by 746
- add_neg_cancelproof · cited by 213
Cited by76
Results whose statement or proof uses this declaration.
- Set.image_add_leftproof · cited by 44
- sub_sub_cancel_leftproof · cited by 28
- neg_add_cancel_commproof · cited by 17
- eq_neg_add_iff_add_eqproof · cited by 16
- mem_leftAddCoset_iffproof · cited by 9
- AddSubgroup.comap_map_eqproof · cited by 8
- neg_add_eq_iff_eq_addproof · cited by 7
- neg_add_le_iff_le_addproof · cited by 6
- neg_add_lt_iff_lt_addproof · cited by 6
- add_left_surjectiveproof · cited by 6
- AddSubgroup.isOpen_of_mem_nhdsproof · cited by 5
- add_eq_of_eq_sub'proof · cited by 4