Theorems · Theorem · group theory
Finset.prod_union
∀ {ι : Type u_1} {M : Type u_4} {s₁ s₂ : Finset ι} [inst : CommMonoid M] {f : ι → M} [inst_1 : DecidableEq ι],
Disjoint s₁ s₂ → ∏ x ∈ s₁ ∪ s₂, f x = (∏ x ∈ s₁, f x) * ∏ x ∈ s₂, f x- Cited by
- 31 results in Mathlib
- Foundations
- Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommMonoidDecidableEq
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.
- Finsetstatement and proof · cited by 13,712
- mul_oneproof · cited by 3,885
- Finset.prodstatement and proof · cited by 2,356
- CommMonoidstatement and proof · cited by 2,264
- Disjointstatement and proof · cited by 2,201
- Finset.prod_union_interproof · cited by 4
- Finset.disjoint_iff_inter_eq_emptyproof · cited by 4
Cited by31
Results whose statement or proof uses this declaration.
- Finset.prod_le_prod_of_subset_of_one_le'proof · cited by 12
- Finset.prod_sdiffproof · cited by 10
- ProbabilityTheory.Kernel.iIndepFun.indepFun_finsetproof · cited by 8
- Finset.prod_filter_mul_prod_filter_notproof · cited by 6
- multipliable_one_add_of_summableproof · cited by 4
- Finsupp.prod_dvd_prod_of_subset_of_dvdproof · cited by 4
- cauchySeq_finset_iff_prod_vanishingproof · cited by 3
- Finset.prod_le_prod_of_subset_of_one_leproof · cited by 2
- HasProd.congr_cofinite₀proof · cited by 2
- HasProd.nat_mul_neg_add_oneproof · cited by 2
- Finset.prod_sdiff_eq_prod_sdiff_iffproof · cited by 2
- MeasureTheory.Measure.pi_prod_map_IicProdIocproof · cited by 1