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Theorems · Theorem · order theory

Nat.cast_nonpos

∀ {α : Type u_1} [inst : AddMonoidWithOne α] [inst_1 : PartialOrder α] [AddLeftMono α] [ZeroLEOneClass α] [CharZero α]
  {n : ℕ}, ↑n ≤ 0 ↔ n = 0
Defined in
Mathlib.Data.Nat.Cast.Order.Basic
Cited by
1 results in Mathlib
Foundations
Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AddMonoidWithOnePartialOrderAddLeftMonoZeroLEOneClassCharZero
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Around this declaration

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

covByVAdd_zero · cited by 0covByVAdd_zeroPartialOrder · cited by 6410PartialOrderNat.cast_zero · cited by 1870Nat.cast_zeroCharZero · cited by 932CharZeroAddLeftMono · cited by 687AddLeftMonoAddMonoidWithOne · cited by 313AddMonoidWithOneZeroLEOneClass · cited by 304ZeroLEOneClassNat.cast_nonposCITED BYCITES

Cites6

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Cited by1

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