Theorems · Theorem · group theory
Finset.prod_div_distrib
∀ {ι : Type u_1} {G : Type u_5} {s : Finset ι} [inst : DivisionCommMonoid G] (f g : ι → G),
∏ x ∈ s, f x / g x = (∏ x ∈ s, f x) / ∏ x ∈ s, g x- Cited by
- 9 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext, Quot.sound
- Assumes
- DivisionCommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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 · cited by 2,356
- DivisionCommMonoidstatement and proof · cited by 80
- Multiset.prod_map_divproof · cited by 2
Cited by9
Results whose statement or proof uses this declaration.
- commProb_piproof · cited by 3
- Real.Wallis.W_eq_integral_sin_pow_div_integral_sin_powproof · cited by 2
- integral_sin_pow_evenproof · cited by 2
- Finset.prod_div_prod_mem_mulSpanproof · cited by 1
- Finset.prod_Ico_int_divproof · cited by 0
- AddDissociated.randomisationproof · cited by 0
- Affine.Triangle.prod_div_one_sub_eq_one_of_mem_line_point_lineMapproof · cited by 0
- cauchySeq_prod_of_eventually_eqproof · cited by 0
- Finset.eq_prod_range_div'proof · cited by 0