Theorems · Theorem · ring theory

SetLike.prod_mem_graded

∀ {ι : Type u_2} {R : Type u_3} {S : Type u_4} [inst : SetLike S R] [inst_1 : CommMonoid R] [inst_2 : AddCommMonoid ι]
  (A : ι → S) [SetLike.GradedMonoid A] {κ : Type u_5} (i : κ → ι) (g : κ → R) {F : Finset κ},
  (∀ k ∈ F, g k ∈ A (i k)) → ∏ k ∈ F, g k ∈ A (∑ k ∈ F, i k)

Defined in

Mathlib.Algebra.GradedMonoid

Cited by

1 results in Mathlib

Foundations

Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SetLikeCommMonoidAddCommMonoidSetLike.GradedMonoid