Theorems · Theorem · ring theory
Nat.cast_prod
∀ {R : Type u_4} {ι : Type u_5} [inst : CommSemiring R] (f : ι → ℕ) (s : Finset ι), ↑(∏ i ∈ s, f i) = ∏ i ∈ s, ↑(f i)- Defined in
- Mathlib.Algebra.BigOperators.Ring.Finset
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Quot.sound
- Assumes
- CommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- CommSemiringstatement and proof · cited by 10,911
- Finset.prodstatement · cited by 2,356
- map_prodproof · cited by 108
- Nat.castRingHomproof · cited by 27
Cited by15
Results whose statement or proof uses this declaration.
- Int.radical_natAbs_eq_radicalproof · cited by 3
- MeasureTheory.hausdorffMeasure_pi_realproof · cited by 3
- Choose.choose_modEq_prod_range_chooseproof · cited by 2
- iter_deriv_invproof · cited by 2
- Complex.GammaSeq_mulproof · cited by 1
- Chebyshev.theta_eq_log_primorialproof · cited by 1
- Chebyshev.psi_eq_log_lcmUptoproof · cited by 1
- Nat.cast_finsuppProdproof · cited by 1
- Int.radical_natCastproof · cited by 0
- Nat.prod_modEq_iteproof · cited by 0
- Nat.prod_modEq_singleproof · cited by 0
- Nat.totient_eq_mul_prod_factorsproof · cited by 0