Theorems · Theorem · ring theory
Finset.prod_natCast
∀ {ι : Type u_1} {R : Type u_4} [inst : CommSemiring R] (s : Finset ι) (f : ι → ℕ), ↑(∏ i ∈ s, f i) = ∏ i ∈ s, ↑(f i)- Defined in
- Mathlib.Algebra.BigOperators.Ring.Finset
- Cited by
- 8 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 by8
Results whose statement or proof uses this declaration.
- Polynomial.Chebyshev.iterate_derivative_U_eval_oneproof · cited by 3
- Polynomial.Chebyshev.iterate_derivative_T_eval_oneproof · cited by 2
- ZMod.wilsons_lemmaproof · cited by 2
- Finset.prod_range_natCast_subproof · cited by 0
- Nat.factorial_coe_dvd_prodproof · cited by 0
- tendsto_factorial_div_pow_self_atTopproof · cited by 0
- ZMod.prod_Ico_one_primeproof · cited by 0
- Matrix.det_vandermonde_id_eq_superFactorialproof · cited by 0