Theorems · Theorem · group theory
Finset.prod_sdiff
∀ {ι : Type u_1} {M : Type u_4} {s₁ s₂ : Finset ι} [inst : CommMonoid M] {f : ι → M} [inst_1 : DecidableEq ι],
s₁ ⊆ s₂ → (∏ x ∈ s₂ \ s₁, f x) * ∏ x ∈ s₁, f x = ∏ x ∈ s₂, f x- Cited by
- 10 results in Mathlib
- Foundations
- Depth 65 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.
Cites6
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.prodstatement and proof · cited by 2,356
- CommMonoidstatement and proof · cited by 2,264
- Finset.prod_unionproof · cited by 31
- Finset.sdiff_disjointproof · cited by 20
- Finset.sdiff_union_of_subsetproof · cited by 12
Cited by10
Results whose statement or proof uses this declaration.
- Finset.prod_subset_one_on_sdiffproof · cited by 4
- cauchySeq_finset_iff_prod_vanishingproof · cited by 3
- Finset.prod_involutionproof · cited by 2
- MvPowerSeries.coeff_eq_zero_of_constantCoeff_nilpotentproof · cited by 2
- ArithmeticFunction.tendsTo_eulerProduct_of_tendsToproof · cited by 1
- Nat.prod_primeFactors_sdiff_of_squarefreeproof · cited by 1
- Polynomial.X_pow_sub_one_mul_prod_cyclotomic_eq_X_pow_sub_one_of_dvdproof · cited by 1
- Polynomial.eval_one_cyclotomic_not_prime_powproof · cited by 1
- Finset.prod_sdiff_div_prod_sdiffproof · cited by 0
- Finset.prod_sdiff_eq_divproof · cited by 0