Theorems · Theorem · group theory
finprod_mem_def
∀ {α : Type u_1} {M : Type u_5} [inst : CommMonoid M] (s : Set α) (f : α → M),
∏ᶠ (a : α) (_ : a ∈ s), f a = ∏ᶠ (a : α), s.mulIndicator f a- Defined in
- Mathlib.Algebra.BigOperators.Finprod
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommMonoid
Around this declaration
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
- CommMonoidstatement and proof · cited by 2,264
- finprodstatement · cited by 257
- Set.mulIndicatorstatement · cited by 163
- finprod_congrproof · cited by 8
- finprod_eq_mulIndicator_applyproof · cited by 3
Cited by5
Results whose statement or proof uses this declaration.
- finprod_cond_eq_prod_of_cond_iffproof · cited by 6
- finprod_mem_inter_mulSupportproof · cited by 3
- finprod_mem_eq_one_of_infiniteproof · cited by 1
- finprod_mem_mul_distrib'proof · cited by 1
- finprod_mem_mulSupportproof · cited by 0