Theorems · Theorem · order theory
HahnSeries.archimedeanClassMk_le_archimedeanClassMk_iff_of_orderTop_ofLex
∀ {Γ : Type u_1} {R : Type u_2} [inst : LinearOrder Γ] [inst_1 : LinearOrder R] [inst_2 : AddCommGroup R]
[inst_3 : IsOrderedAddMonoid R] {x y : Lex (HahnSeries Γ R)},
(ofLex x).orderTop = (ofLex y).orderTop →
(ArchimedeanClass.mk x ≤ ArchimedeanClass.mk y ↔
ArchimedeanClass.mk (ofLex x).leadingCoeff ≤ ArchimedeanClass.mk (ofLex y).leadingCoeff)- Defined in
- Mathlib.RingTheory.HahnSeries.Lex
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites41
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
- AddCommGroupstatement and proof · cited by 12,871
- Top.topproof · cited by 9,680
- LinearOrderstatement and proof · cited by 8,572
- Equivstatement · cited by 8,337
- PartialOrderproof · cited by 6,410
- WithTopstatement and proof · cited by 3,754
- LT.lt.leproof · cited by 2,189
- absproof · cited by 1,814
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- WithTop.someproof · cited by 1,128
- eq_or_neproof · cited by 1,117
Cited by1
Results whose statement or proof uses this declaration.
- HahnSeries.archimedeanClassMk_le_archimedeanClassMk_iffproof · cited by 1