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Theorems · Theorem · order theory

FiniteArchimedeanClass.mk_lt_mk

∀ {M : Type u_1} [inst : AddCommGroup M] [inst_1 : LinearOrder M] [inst_2 : IsOrderedAddMonoid M] {a : M} (ha : a ≠ 0)
  {b : M} (hb : b ≠ 0),
  FiniteArchimedeanClass.mk a ha < FiniteArchimedeanClass.mk b hb ↔ ArchimedeanClass.mk a < ArchimedeanClass.mk b
Defined in
Mathlib.Algebra.Order.Archimedean.Class
Cited by
1 results in Mathlib
Foundations
Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AddCommGroupLinearOrderIsOrderedAddMonoid
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Around this declaration

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

HahnEmbedding.Partial.eval_ne · cited by 1Partial.eval_neAddCommGroup · cited by 12871AddCommGroupTop.top · cited by 9680Top.topLinearOrder · cited by 8572LinearOrderIsOrderedAddMonoid · cited by 1659IsOrderedAddMonoidArchimedeanClass · cited by 247ArchimedeanClassArchimedeanClass.mk · cited by 174ArchimedeanClass.mkFiniteArchimedeanClass · cited by 100FiniteArchimedeanClassFiniteArchimedeanClass.mk · cited by 28FiniteArchimedeanClass.mkFiniteArchimedeanClass.mk_lt_…CITED BYCITES

Cites8

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Cited by1

Results whose statement or proof uses this declaration.