Theorems · Definition · group theory
AddEquiv.piAddUnits
{ι : Type u_1} →
{M : ι → Type u_2} → [inst : (i : ι) → AddMonoid (M i)] → AddUnits ((i : ι) → M i) ≃+ ((i : ι) → AddUnits (M i))The additive-monoid equivalence between (additive) units of a product, and the product of the (additive) units of each monoid.
- Defined in
- Mathlib.Algebra.Group.Pi.Units
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses Quot.sound
- Assumes
- AddMonoid
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.
- AddMonoidstatement and proof · cited by 2,864
- AddEquivstatement · cited by 1,087
- AddUnitsstatement and proof · cited by 325
- AddUnits.valproof · cited by 248
- AddUnits.negproof · cited by 14
Cited by6
Results whose statement or proof uses this declaration.
- AddEquiv.val_neg_piAddUnits_applystatement and proof · cited by 1
- AddEquiv.val_neg_piAddUnits_symm_applystatement and proof · cited by 0
- AddEquiv.val_piAddUnits_applystatement and proof · cited by 0
- AddEquiv.val_piAddUnits_symm_applystatement and proof · cited by 0
- ContinuousAddEquiv.piAddUnitsproof · cited by 0
- IsAddUnit.val_neg_applyproof · cited by 0