Theorems · Theorem · group theory
neg_add_cancel_left
∀ {G : Type u_1} [inst : AddGroup G] (a b : G), -a + (a + b) = b- Defined in
- Mathlib.Algebra.Group.Defs
- Cited by
- 84 results in Mathlib
- Foundations
- Depth 7 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
- neg_add_cancelproof · cited by 256
Cited by84
Results whose statement or proof uses this declaration.
- add_sub_cancel_leftproof · cited by 198
- Set.image_add_leftproof · cited by 44
- eq_neg_add_iff_add_eqproof · cited by 16
- add_neg_cancel_commproof · cited by 14
- mem_leftAddCoset_iffproof · cited by 9
- IsUltrametricDist.isNonarchimedean_normproof · cited by 8
- sub_le_sub_iff_leftproof · cited by 8
- add_mem_cancel_leftproof · cited by 8
- neg_add_eq_iff_eq_addproof · cited by 7
- Irrational.ratCast_addproof · cited by 6
- AddSubgroup.normalizer_eq_top_iffproof · cited by 6
- Complex.arg_mem_Iocproof · cited by 6