Theorems · Theorem · number theory
Nat.Prime.ne_one
∀ {p : ℕ}, Nat.Prime p → p ≠ 1- Defined in
- Mathlib.Data.Nat.Prime.Defs
- Cited by
- 61 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Nat.Primestatement and proof · cited by 2,059
- LT.lt.ne'proof · cited by 1,417
- Nat.Prime.one_ltproof · cited by 118
Cited by61
Results whose statement or proof uses this declaration.
- Nat.prime_iff_prime_intproof · cited by 27
- padicValNat_eq_emultiplicityproof · cited by 9
- Polynomial.cyclotomic_primeproof · cited by 7
- Nat.primeFactors_oneproof · cited by 6
- padicNorm.dvd_iff_norm_leproof · cited by 5
- Nat.Prime.properDivisorsproof · cited by 4
- ArithmeticFunction.moebius_mul_coe_zetaproof · cited by 4
- Nat.primeFactors_prodproof · cited by 3
- Function.minimalPeriod_eq_prime_iffproof · cited by 3
- CharP.isUnit_natCast_iffproof · cited by 3
- Squarefree.natFactorization_le_oneproof · cited by 3
- padicValRat.defnproof · cited by 2