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Theorems · Theorem · group theory

SubmonoidClass.coe_list_prod

∀ {M : Type u_1} {B : Type u_3} [inst : Monoid M] [inst_1 : SetLike B M] [inst_2 : SubmonoidClass B M] {S : B}
  (l : List ↥S), ↑l.prod = (List.map Subtype.val l).prod
Defined in
Mathlib.Algebra.Group.Submonoid.BigOperators
Cited by
2 results in Mathlib
Foundations
Depth 16 from the axioms · uses propext
Assumes
MonoidSetLikeSubmonoidClass
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

list_prod_mem · cited by 9list_prod_memSubgroup.val_list_prod · cited by 1Subgroup.val_list_prodMonoid · cited by 3887MonoidSetLike · cited by 1084SetLikeSubmonoidClass · cited by 60SubmonoidClassmap_list_prod · cited by 35map_list_prodSubmonoidClass.subtype · cited by 11SubmonoidClass.subtypeSubmonoidClass.coe_list_prodCITED BYCITES

Cites5

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Cited by2

Results whose statement or proof uses this declaration.