Theorems · Definition · group theory

Set.commMonoid

{α : Type u_2} → [CommMonoid α] → CommMonoid (Set α)

Set α is a CommMonoid under pointwise operations if α is.

Defined in: Mathlib.Algebra.Group.Pointwise.Set.Basic
Cited by: 21 results in Mathlib
Foundations: Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommMonoid

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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.

Setstatement and proof · cited by 53,352
Monoidproof · cited by 3,887
CommMonoidstatement and proof · cited by 2,264
CommSemigroupproof · cited by 62
Set.monoidproof · cited by 19
Set.commSemigroupproof · cited by 0

Cited by21

Results whose statement or proof uses this declaration.

Set.mem_finsetProdstatement · cited by 3
Set.finsetProd_singletonstatement · cited by 2
Set.image_finsetProd_pistatement · cited by 2
Submodule.prod_spanstatement · cited by 2
Set.image_multiset_prodstatement · cited by 1
Set.multiset_prod_mem_multiset_prodstatement · cited by 1
Set.multiset_prod_subset_multiset_prodstatement · cited by 1
Set.finsetProd_mem_finsetProdstatement · cited by 1
Set.finsetProd_subset_finsetProdstatement · cited by 1
Set.image_finsetProdstatement · cited by 1
Ideal.prod_spanstatement · cited by 0
Finset.coe_prodstatement · cited by 0