Theorems · Theorem · order theory
ArchimedeanClass.mk_ratCast_nonneg
∀ {R : Type u_1} [inst : LinearOrder R] [inst_1 : Field R] [inst_2 : IsOrderedRing R] (q : ℚ),
0 ≤ ArchimedeanClass.mk ↑q- Defined in
- Mathlib.Algebra.Order.Ring.Archimedean
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LinearOrderstatement and proof · cited by 8,572
- Fieldstatement and proof · cited by 7,404
- le_reflproof · cited by 2,061
- eq_or_neproof · cited by 1,117
- IsOrderedRingstatement and proof · cited by 777
- ArchimedeanClassstatement and proof · cited by 247
- ArchimedeanClass.mkstatement and proof · cited by 174
- Rat.cast_zeroproof · cited by 29
- ArchimedeanClass.mk_ratCastproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- ArchimedeanClass.stdPart_ratCastproof · cited by 1
- ArchimedeanClass.FiniteResidueField.mk_ratCastproof · cited by 1
- ArchimedeanClass.FiniteElement.mk_ratCaststatement · cited by 1