Theorems · Theorem · group theory
neg_add_cancel_right
∀ {G : Type u_1} [inst : AddGroup G] (a b : G), a + -b + b = a- Defined in
- Mathlib.Algebra.Group.Defs
- Cited by
- 75 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
- add_zeroproof · cited by 2,707
- add_assocproof · cited by 746
- neg_add_cancelproof · cited by 256
Cited by75
Results whose statement or proof uses this declaration.
- sub_add_cancelproof · cited by 344
- sub_nonnegproof · cited by 167
- sub_posproof · cited by 147
- neg_le_neg_iffproof · cited by 57
- sub_le_iff_le_addproof · cited by 50
- le_sub_iff_add_leproof · cited by 41
- neg_lt_neg_iffproof · cited by 39
- sub_lt_iff_lt_addproof · cited by 39
- Set.image_add_rightproof · cited by 37
- sub_nonposproof · cited by 29
- lt_sub_iff_add_ltproof · cited by 24
- sub_negproof · cited by 22