Theorems · Theorem · number theory
Nat.Prime.one_lt
∀ {p : ℕ}, Nat.Prime p → 1 < p- Defined in
- Mathlib.Data.Nat.Prime.Defs
- Cited by
- 118 results in Mathlib
- Foundations
- Depth 24 from the axioms, rests on 214 definitions · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Nat.Primestatement · cited by 2,059
- Nat.Prime.two_leproof · cited by 53
Cited by118
Results whose statement or proof uses this declaration.
- Nat.Prime.ne_oneproof · cited by 61
- ringExpChar.eqproof · cited by 15
- Nat.Prime.one_leproof · cited by 12
- Nat.Prime.not_coprime_iff_dvdproof · cited by 9
- PadicInt.exists_pow_neg_ltproof · cited by 6
- exists_prime_orderOf_dvd_cardproof · cited by 5
- padicNorm.dvd_iff_norm_leproof · cited by 5
- IsCyclotomicExtension.Rat.inertiaDeg_span_zeta_sub_oneproof · cited by 4
- Nat.prime_def_minFacproof · cited by 4
- IsCyclotomicExtension.discr_prime_pow_ne_twoproof · cited by 4
- IsPrimitiveRoot.norm_pow_sub_one_of_prime_pow_ne_twoproof · cited by 4
- Padic.norm_intCast_lt_one_iffproof · cited by 3