Theorems · Theorem · group theory
IsAddUnit.add
∀ {M : Type u_1} [inst : AddMonoid M] {a b : M}, IsAddUnit a → IsAddUnit b → IsAddUnit (a + b)- Defined in
- Mathlib.Algebra.Group.Units.Defs
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 9 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
- AddUnitsproof · cited by 325
- AddUnits.valproof · cited by 248
- IsAddUnitstatement and proof · cited by 215
Cited by11
Results whose statement or proof uses this declaration.
- IsAddUnit.add_iffproof · cited by 2
- IsAddUnit.sub_eq_sub_iffproof · cited by 2
- AddUnits.isAddUnit_addUnits_addproof · cited by 1
- AddUnits.isAddUnit_add_addUnitsproof · cited by 1
- AddCommute.sub_eq_sub_iff_of_isAddUnitproof · cited by 1
- AddCommute.isAddUnit_add_iffproof · cited by 1
- Matrix.isAddUnit_detp_mul_detpproof · cited by 1
- IsAddUnit.subproof · cited by 1
- IsAddUnit.addUnit_addstatement · cited by 0
- Matrix.isAddUnit_detp_smul_mul_adjpproof · cited by 0
- AddCommute.neg_add_eq_neg_add_iff_of_isAddUnitproof · cited by 0