Theorems · Theorem · order theory
Nat.one_lt_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_ltproof · cited by 80
Cited by21
Results whose statement or proof uses this declaration.
- ArithmeticFunction.vonMangoldt_ne_zero_iffproof · cited by 3
- Behrend.nValue_posproof · cited by 3
- Nat.one_lt_ofNatproof · cited by 3
- AddCircle.ergodic_zsmulproof · cited by 2
- MulAction.IsPreprimitive.is_two_motive_of_is_motiveproof · cited by 2
- Real.floor_logb_natCastproof · cited by 2
- Int.one_lt_radical_iffproof · cited by 2
- AkraBazziRecurrence.rpow_p_mul_one_add_smoothingFn_geproof · cited by 1
- AkraBazziRecurrence.rpow_p_mul_one_sub_smoothingFn_leproof · cited by 1
- Behrend.dValue_posproof · cited by 1
- Real.ceil_logb_natCastproof · cited by 1
- Behrend.lower_bound_le_one'proof · cited by 1