Theorems · Theorem · number theory
ZMod.wilsons_lemma
- #51 of the 100 theorems: Wilson’s Lemma
- 1000+ list: Wilson's theorem
∀ (p : ℕ) [inst : Fact (Nat.Prime p)], ↑(p - 1).factorial = -1
Wilson's Lemma: the product of 1, ..., p-1 is -1 modulo p.
- Defined in
- Mathlib.NumberTheory.Wilson
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Fact
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites32
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Finsetproof · cited by 13,712
- Finset.univproof · cited by 3,473
- Unitsproof · cited by 2,804
- Factstatement and proof · cited by 2,726
- Finset.prodproof · cited by 2,356
- Nat.Primestatement and proof · cited by 2,059
- Units.valproof · cited by 1,966
- ZModstatement and proof · cited by 1,024
- Nat.factorialstatement · cited by 616
- Finset.Icoproof · cited by 450
- Finset.mem_univproof · cited by 361
Cited by2
Results whose statement or proof uses this declaration.
- Nat.prime_iff_fac_equiv_neg_oneproof · cited by 0
- ZMod.prod_Ico_one_primeproof · cited by 0