Theorems · Theorem · number theory
Nat.one_lt_radical_iff
∀ {n : ℕ}, 1 < UniqueFactorizationMonoid.radical n ↔ 1 < n- Defined in
- Mathlib.RingTheory.Radical.NatInt
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finset.prodproof · cited by 2,356
- Finset.Nonemptyproof · cited by 1,001
- Nat.primeFactorsproof · cited by 129
- Nat.Prime.one_ltproof · cited by 118
- UniqueFactorizationMonoid.radicalstatement · cited by 64
- Nat.mem_primeFactorsproof · cited by 12
- Nat.radical_eq_prod_primeFactorsproof · cited by 7
- Nat.pos_of_mem_primeFactorsproof · cited by 3
- Finset.one_lt_prod_iff_of_one_leproof · cited by 3
- Nat.nonempty_primeFactorsproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- Int.one_lt_radical_iffproof · cited by 2
- Nat.radical_le_one_iffproof · cited by 1
- Nat.two_le_radical_iffproof · cited by 0