Theorems · Theorem · order theory
ArchimedeanClass.eq_zero_or_top_of_archimedean
∀ {S : Type u_3} [inst : LinearOrder S] [inst_1 : CommRing S] [inst_2 : IsStrictOrderedRing S] [Archimedean S]
(x : ArchimedeanClass S), x = 0 ∨ x = ⊤- Defined in
- Mathlib.Algebra.Order.Ring.Archimedean
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 39 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Top.topstatement and proof · cited by 9,680
- LinearOrderstatement and proof · cited by 8,572
- IsStrictOrderedRingstatement and proof · cited by 2,490
- eq_or_neproof · cited by 1,117
- Archimedeanstatement and proof · cited by 603
- ArchimedeanClassstatement and proof · cited by 247
- ArchimedeanClass.indproof · cited by 3
- ArchimedeanClass.mk_eq_zero_of_archimedeanproof · cited by 2
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