Theorems · Theorem · order theory
ArchimedeanClass.mk_eq_zero_of_archimedean
∀ {S : Type u_3} [inst : LinearOrder S] [inst_1 : CommRing S] [inst_2 : IsStrictOrderedRing S] [Archimedean S] {x : S},
x ≠ 0 → ArchimedeanClass.mk x = 0- Defined in
- Mathlib.Algebra.Order.Ring.Archimedean
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- LinearOrderstatement and proof · cited by 8,572
- IsStrictOrderedRingstatement and proof · cited by 2,490
- one_ne_zeroproof · cited by 885
- Archimedeanstatement and proof · cited by 603
- ArchimedeanClassstatement · cited by 247
- ArchimedeanClass.mkstatement · cited by 174
- ArchimedeanClass.mk_eq_mk_of_archimedeanproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- ArchimedeanClass.mk_map_of_archimedeanproof · cited by 2
- ArchimedeanClass.eq_zero_or_top_of_archimedeanproof · cited by 0