Theorems · Theorem · order theory
Nat.one_le_cast
∀ {α : Type u_1} [inst : AddMonoidWithOne α] [inst_1 : PartialOrder α] [AddLeftMono α] [ZeroLEOneClass α] [CharZero α]
{n : ℕ}, 1 ≤ ↑n ↔ 1 ≤ n- Defined in
- Mathlib.Data.Nat.Cast.Order.Basic
- Cited by
- 21 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- PartialOrderstatement and proof · cited by 6,410
- Nat.cast_oneproof · cited by 2,501
- CharZerostatement and proof · cited by 932
- AddLeftMonostatement and proof · cited by 687
- AddMonoidWithOnestatement and proof · cited by 313
- ZeroLEOneClassstatement and proof · cited by 304
- Nat.cast_leproof · cited by 159
Cited by21
Results whose statement or proof uses this declaration.
- ArithmeticFunction.vonMangoldt_nonnegproof · cited by 6
- NumberField.hermiteTheorem.rank_le_rankOfDiscrBddproof · cited by 4
- Pell.exists_of_not_isSquareproof · cited by 3
- Chebyshev.sum_PrimePow_eq_sum_sum'proof · cited by 2
- setOfPred_liouvilleWith_subset_auxproof · cited by 2
- Behrend.exists_large_sphereproof · cited by 1
- IsApproximateAddSubgroup.card_nsmul_leproof · cited by 1
- LSeries.norm_term_le_of_re_le_reproof · cited by 1
- IsApproximateAddSubgroup.one_leproof · cited by 1
- Nat.one_le_cast_iff_ne_zeroproof · cited by 1
- ExpGrowth.expGrowthSup_powproof · cited by 1
- NumberField.Units.dirichletUnitTheorem.log_le_of_logEmbedding_leproof · cited by 1