Theorems · Theorem · group theory
AddCommute.neg_add_cancel
∀ {G : Type u_1} [inst : AddGroup G] {a b : G}, AddCommute a b → -a + b + a = b- Defined in
- Mathlib.Algebra.Group.Commute.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext
- Assumes
- AddGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- neg_add_cancel_rightproof · cited by 75
- AddCommute.eqproof · cited by 18
- AddCommute.neg_leftproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- AddCommute.neg_add_cancel_assocproof · cited by 0