Theorems · Theorem · group theory
Finset.prod_eq_prod_extend
∀ {ι : Type u_1} {M : Type u_4} {s : Finset ι} [inst : CommMonoid M] (f : ↥s → M),
∏ x, f x = ∏ x ∈ s, Function.extend Subtype.val f 1 xAlso see Finset.prod_ite_mem_eq
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 78 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.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- Finset.univstatement · cited by 3,473
- Finset.prodstatement and proof · cited by 2,356
- CommMonoidstatement and proof · cited by 2,264
- Subtype.val_injectiveproof · cited by 232
- Finset.attachproof · cited by 168
- Function.extendstatement and proof · cited by 111
- Function.Injective.extend_applyproof · cited by 57
- Finset.prod_attachproof · cited by 22
- Finset.univ_eq_attachproof · cited by 13
Cited by3
Results whose statement or proof uses this declaration.
- MeasureTheory.isProjectiveMeasureFamily_piproof · cited by 4
- MeasureTheory.Measure.pi_prod_map_IicProdIocproof · cited by 1
- MeasureTheory.Measure.pi_prod_map_IocProdIocproof · cited by 1