list_prod_mem

∀ {M : Type u_1} {B : Type u_3} [inst : Monoid M] [inst_1 : SetLike B M] [SubmonoidClass B M] {S : B} {l : List M},
  (∀ x ∈ l, x ∈ S) → l.prod ∈ S

Product of a list of elements in a submonoid is in the submonoid.

Defined in: Mathlib.Algebra.Group.Submonoid.BigOperators
Cited by: 9 results in Mathlib
Foundations: Depth 59 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Monoid SetLike SubmonoidClass

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