Theorems · Theorem · order theory
Nat.cast_nonneg
∀ {α : Type u_3} [inst : Semiring α] [inst_1 : PartialOrder α] [IsOrderedRing α] (n : ℕ), 0 ≤ ↑nSpecialisation of Nat.cast_nonneg', which seems to be easier for Lean to use.
- Defined in
- Mathlib.Data.Nat.Cast.Order.Ring
- Cited by
- 109 results in Mathlib
- Foundations
- Depth 27 from the axioms, rests on 266 definitions · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- PartialOrderstatement and proof · cited by 6,410
- IsOrderedRingstatement and proof · cited by 777
- Nat.cast_nonneg'proof · cited by 245
Cited by109
Results whose statement or proof uses this declaration.
- Nat.abs_castproof · cited by 36
- RCLike.norm_natCastproof · cited by 19
- Nat.floor_natCastproof · cited by 19
- ENNReal.rpow_natCastproof · cited by 18
- ENNReal.toReal_natCastproof · cited by 15
- Complex.norm_natCastproof · cited by 12
- integral_powproof · cited by 8
- Real.norm_natCastproof · cited by 6
- NNRat.cast_nonnegproof · cited by 6
- Real.sqrtTwoAddSeries_step_upproof · cited by 5
- Complex.natCast_logproof · cited by 5
- summable_riemannZetaSummandproof · cited by 4