Theorems · Theorem · order theory
ArchimedeanClass.mk_natCast_nonneg
∀ {S : Type u_3} [inst : LinearOrder S] [inst_1 : CommRing S] [inst_2 : IsStrictOrderedRing S] (n : ℕ),
0 ≤ ArchimedeanClass.mk ↑n- Defined in
- Mathlib.Algebra.Order.Ring.Archimedean
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 46 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.
- CommRingstatement and proof · cited by 17,173
- LinearOrderstatement and proof · cited by 8,572
- IsStrictOrderedRingstatement and proof · cited by 2,490
- Int.cast_natCastproof · cited by 393
- ArchimedeanClassstatement · cited by 247
- ArchimedeanClass.mkstatement and proof · cited by 174
- ArchimedeanClass.mk_intCast_nonnegproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- ArchimedeanClass.FiniteElement.mk_natCaststatement · cited by 1
- ArchimedeanClass.FiniteResidueField.mk_ratCastproof · cited by 1