Theorems · Theorem · number theory
Nat.prod_modEq_ite
∀ {α : Type u_1} {n : ℕ} {f : α → ℕ} [inst : DecidableEq α] {s : Finset α} {a : α},
(∀ x ∈ s, x ≠ a → f x ≡ 1 [MOD n]) → ∏ x ∈ s, f x ≡ if a ∈ s then f a else 1 [MOD n]- Defined in
- Mathlib.Algebra.BigOperators.ModEq
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEq
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
- Nat.cast_oneproof · cited by 2,501
- Finset.prodstatement and proof · cited by 2,356
- ZModproof · cited by 1,024
- Nat.ModEqstatement and proof · cited by 225
- Nat.cast_prodproof · cited by 15
- Finset.prod_eq_iteproof · cited by 2
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