Theorems · Theorem · field theory
ArchimedeanClass.FiniteResidueField.mk_eq_zero
∀ {K : Type u_1} [inst : LinearOrder K] [inst_1 : Field K] [inst_2 : IsOrderedRing K]
{x : ArchimedeanClass.FiniteElement K}, ArchimedeanClass.FiniteResidueField.mk x = 0 ↔ 0 < ArchimedeanClass.mk ↑x- Defined in
- Mathlib.Algebra.Order.Ring.StandardPart
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- LinearOrderstatement and proof · cited by 8,572
- Equivstatement · cited by 8,337
- Fieldstatement and proof · cited by 7,404
- sub_zeroproof · cited by 938
- OrderDualstatement · cited by 927
- Multiplicativestatement · cited by 875
- Valuationstatement · cited by 823
- IsOrderedRingstatement and proof · cited by 777
- ArchimedeanClassstatement · cited by 247
- ValuationSubringstatement · cited by 187
- ArchimedeanClass.mkstatement and proof · cited by 174
Cited by3
Results whose statement or proof uses this declaration.
- ArchimedeanClass.stdPart_eq_zeroproof · cited by 6
- ArchimedeanClass.FiniteResidueField.mk_ne_zeroproof · cited by 2
- ArchimedeanClass.mk_sub_pos_iffproof · cited by 2