Theorems · Theorem · group theory
AddUnits.add_neg
∀ {α : Type u} [inst : AddMonoid α] (a : AddUnits α), ↑a + ↑(-a) = 0- Defined in
- Mathlib.Algebra.Group.Units.Defs
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
- Assumes
- AddMonoid
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.
- AddMonoidstatement and proof · cited by 2,864
- AddUnitsstatement and proof · cited by 325
- AddUnits.valstatement · cited by 248
- AddUnits.val_negproof · cited by 3
Cited by19
Results whose statement or proof uses this declaration.
- AddUnits.add_neg_cancel_rightproof · cited by 8
- AddUnits.val_neg_eq_neg_valproof · cited by 8
- IsAddUnit.add_neg_cancelproof · cited by 5
- AddUnits.add_neg_cancel_leftproof · cited by 3
- IsAddUnit.val_neg_addproof · cited by 3
- Set.isAddUnit_iffproof · cited by 2
- IsAddUnit.add_val_negproof · cited by 2
- AddUnits.addCommute_coe_negproof · cited by 1
- Finset.isAddUnit_iffproof · cited by 1
- AddUnits.range_embedProductproof · cited by 1
- AddUnits.add_neg_of_eqproof · cited by 1
- AddUnits.isAddRegularproof · cited by 1