Theorems · Theorem · field theory
ArchimedeanClass.FiniteResidueField.mk_lt_mk
∀ {K : Type u_1} [inst : LinearOrder K] [inst_1 : Field K] [inst_2 : IsOrderedRing K]
{x y : ArchimedeanClass.FiniteElement K},
ArchimedeanClass.FiniteResidueField.mk x < ArchimedeanClass.FiniteResidueField.mk y ↔
x < y ∧ ArchimedeanClass.FiniteResidueField.mk x ≠ ArchimedeanClass.FiniteResidueField.mk y- Defined in
- Mathlib.Algebra.Order.Ring.StandardPart
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 96 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.
- DFunLike.coestatement and proof · cited by 62,936
- LinearOrderstatement and proof · cited by 8,572
- Fieldstatement and proof · cited by 7,404
- IsOrderedRingstatement and proof · cited by 777
- OrderRingHomstatement · cited by 132
- ArchimedeanClass.FiniteElementstatement and proof · cited by 36
- ArchimedeanClass.FiniteResidueField.mkstatement and proof · cited by 22
- ArchimedeanClass.FiniteResidueFieldstatement · cited by 17
- Quotient.eq_iff_equivproof · cited by 6
- Quotient.mk_lt_mkproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- ArchimedeanClass.FiniteResidueField.lt_of_mk_lt_mkproof · cited by 0