Theorems · Theorem · group theory
AddUnits.val_neg_eq_neg_val
∀ {α : Type u} [inst : SubtractionMonoid α] (u : AddUnits α), ↑(-u) = -↑u- Defined in
- Mathlib.Algebra.Group.Units.Defs
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses no axioms
- Assumes
- SubtractionMonoid
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.
- AddUnitsstatement and proof · cited by 325
- AddUnits.valstatement · cited by 248
- SubtractionMonoidstatement and proof · cited by 208
- AddUnits.add_negproof · cited by 19
- neg_eq_of_add_eq_zero_rightproof · cited by 9
Cited by8
Results whose statement or proof uses this declaration.
- IsAddUnit.add_neg_cancelproof · cited by 5
- IsAddUnit.negproof · cited by 3
- IsAddUnit.neg_add_cancelproof · cited by 2
- AddUnits.val_sub_eq_sub_valproof · cited by 1
- AddSubgroup.mem_addUnits_iff_val_memproof · cited by 1
- IsAddUnit.addUnit_negproof · cited by 0
- Algebra.GrothendieckAddGroup.lift_applyproof · cited by 0
- AddUnits.embedding_val_mkproof · cited by 0