Theorems · Theorem · order theory
ArchimedeanClass.mk_ratCast
∀ {R : Type u_1} [inst : LinearOrder R] [inst_1 : Field R] [inst_2 : IsOrderedRing R] {q : ℚ},
q ≠ 0 → ArchimedeanClass.mk ↑q = 0- Defined in
- Mathlib.Algebra.Order.Ring.Archimedean
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- IsOrderedRingstatement and proof · cited by 777
- ArchimedeanClassstatement · cited by 247
- ArchimedeanClass.mkstatement and proof · cited by 174
- Rat.cast_oneproof · cited by 52
- Rat.castHomproof · cited by 33
- eq_ratCastproof · cited by 26
- RingHom.toAddMonoidHomproof · cited by 17
- ArchimedeanClass.mk_map_of_archimedeanproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- ArchimedeanClass.mk_ratCast_nonnegproof · cited by 3