Theorems · Theorem · group theory
AddCommute.add_neg_cancel
∀ {G : Type u_1} [inst : AddGroup G] {a b : G}, AddCommute a b → a + b + -a = b- Defined in
- Mathlib.Algebra.Group.Commute.Defs
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 10 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
- AddCommutestatement and proof · cited by 185
- add_neg_cancel_rightproof · cited by 65
- AddCommute.eqproof · cited by 18
Cited by1
Results whose statement or proof uses this declaration.
- AddCommute.add_neg_cancel_assocproof · cited by 0