Theorems · Theorem · group theory
IsAddUnit.neg_add_cancel
∀ {α : Type u} [inst : SubtractionMonoid α] {a : α}, IsAddUnit a → -a + a = 0- Defined in
- Mathlib.Algebra.Group.Units.Defs
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses no axioms
- Assumes
- SubtractionMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddUnitsproof · cited by 325
- AddUnits.valproof · cited by 248
- IsAddUnitstatement and proof · cited by 215
- SubtractionMonoidstatement and proof · cited by 208
- AddUnits.neg_addproof · cited by 17
- AddUnits.val_neg_eq_neg_valproof · cited by 8
Cited by3
Results whose statement or proof uses this declaration.
- IsAddUnit.addUnit'proof · cited by 11
- IsAddUnit.eq_on_negproof · cited by 1
- IsAddUnit.zero_sub_add_cancelproof · cited by 0