Theorems · Theorem · order theory
Nat.cast_lt_one
∀ {α : Type u_1} [inst : AddMonoidWithOne α] [inst_1 : PartialOrder α] [AddLeftMono α] [ZeroLEOneClass α] [CharZero α]
{n : ℕ}, ↑n < 1 ↔ n = 0- Defined in
- Mathlib.Data.Nat.Cast.Order.Basic
- Cited by
- 2 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 by2
Results whose statement or proof uses this declaration.
- MvPowerSeries.one_le_order_iff_constCoeff_eq_zeroproof · cited by 2
- PowerSeries.one_le_order_iff_constCoeff_eq_zeroproof · cited by 2