Theorems · Definition · order theory
ArchimedeanClass.addValuation
(R : Type u_1) →
[inst : LinearOrder R] →
[inst_1 : CommRing R] → [inst_2 : IsStrictOrderedRing R] → AddValuation R (ArchimedeanClass R)ArchimedeanClass.mk defines an AddValuation on the ring R.
- Defined in
- Mathlib.Algebra.Order.Ring.Archimedean
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 41 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- ArchimedeanClassstatement · cited by 247
- ArchimedeanClass.mkproof · cited by 174
- AddValuationstatement · cited by 96
- AddValuation.ofproof · cited by 2
- ArchimedeanClass.mk_mulproof · cited by 1
Cited by16
Results whose statement or proof uses this declaration.
- ArchimedeanClass.FiniteElementproof · cited by 36
- ArchimedeanClass.FiniteResidueField.mk_eq_zerostatement · cited by 3
- ArchimedeanClass.FiniteElement.extstatement · cited by 2
- ArchimedeanClass.FiniteResidueField.mk_ne_zerostatement · cited by 2
- ArchimedeanClass.stdPart_addproof · cited by 2
- ArchimedeanClass.FiniteElement.not_isUnit_iff_mk_posstatement · cited by 2
- ArchimedeanClass.stdPart_mulproof · cited by 1
- ArchimedeanClass.FiniteResidueField.mk_eq_mkstatement · cited by 1
- ArchimedeanClass.FiniteElement.ext_iffstatement · cited by 0
- ArchimedeanClass.FiniteElement.isUnit_iff_mk_eq_zerostatement · cited by 0
- ArchimedeanClass.addValuation_applystatement · cited by 0
- ArchimedeanClass.FiniteElement.val_addstatement · cited by 0