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Theorems · Theorem · field theory

ArchimedeanClass.FiniteElement.mk_le_mk

∀ {K : Type u_1} [inst : LinearOrder K] [inst_1 : Field K] [inst_2 : IsOrderedRing K] (x y : K)
  (hx : 0 ≤ ArchimedeanClass.mk x) (hy : 0 ≤ ArchimedeanClass.mk y),
  ArchimedeanClass.FiniteElement.mk x hx ≤ ArchimedeanClass.FiniteElement.mk y hy ↔ x ≤ y
Defined in
Mathlib.Algebra.Order.Ring.StandardPart
Cited by
1 results in Mathlib
Foundations
Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
LinearOrderFieldIsOrderedRing
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

ArchimedeanClass.stdPart_monotoneOn · cited by 0ArchimedeanClass.stdPart_…LinearOrder · cited by 8572LinearOrderField · cited by 7404FieldIsOrderedRing · cited by 777IsOrderedRingArchimedeanClass · cited by 247ArchimedeanClassArchimedeanClass.mk · cited by 174ArchimedeanClass.mkArchimedeanClass.FiniteElement · cited by 36ArchimedeanClass.FiniteEl…ArchimedeanClass.FiniteElement.mk · cited by 23FiniteElement.mkFiniteElement.mk_le_mkCITED BYCITES

Cites7

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Cited by1

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