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Theorems · Theorem · order theory

Nat.ofNat_le_cast

∀ {α : Type u_1} [inst : AddMonoidWithOne α] [inst_1 : PartialOrder α] [AddLeftMono α] [ZeroLEOneClass α] [CharZero α]
  {m n : ℕ} [inst_5 : m.AtLeastTwo], OfNat.ofNat m ≤ ↑n ↔ OfNat.ofNat m ≤ n
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
Assumes
AddMonoidWithOnePartialOrderAddLeftMonoZeroLEOneClassCharZeroNat.AtLeastTwo
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Real.qaryEntropy_strictAntiOn · cited by 1Real.qaryEntropy_strictAn…Real.qaryEntropy_strictMonoOn · cited by 1Real.qaryEntropy_strictMo…PartialOrder · cited by 6410PartialOrderCharZero · cited by 932CharZeroAddLeftMono · cited by 687AddLeftMonoNat.AtLeastTwo · cited by 405Nat.AtLeastTwoAddMonoidWithOne · cited by 313AddMonoidWithOneZeroLEOneClass · cited by 304ZeroLEOneClassNat.cast_le · cited by 159Nat.cast_leNat.ofNat_le_castCITED BYCITES

Cites7

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Cited by2

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