Theorems · Theorem · group theory
Finset.univ_prod_mulSingle
∀ {I : Type u_7} [inst : DecidableEq I] {M : I → Type u_8} [inst_1 : (i : I) → CommMonoid (M i)] [inst_2 : Fintype I]
(f : (i : I) → M i), ∏ i, Pi.mulSingle i (f i) = f- Defined in
- Mathlib.Algebra.BigOperators.Pi
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEqCommMonoidFintype
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fintypestatement and proof · cited by 7,736
- Finset.univstatement and proof · cited by 3,473
- Finset.prodstatement · cited by 2,356
- CommMonoidstatement and proof · cited by 2,264
- Pi.mulSinglestatement and proof · cited by 111
- Finset.prod_applyproof · cited by 70
- Finset.prod_pi_mulSingleproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- MonoidHom.functions_extproof · cited by 1
- Pi.mulSingle_inductionproof · cited by 0