Theorems · Theorem · order theory
archimedean_iff_nat_le
∀ {K : Type u_4} [inst : Field K] [inst_1 : LinearOrder K] [IsStrictOrderedRing K],
Archimedean K ↔ ∀ (x : K), ∃ n, x ≤ ↑n- Defined in
- Mathlib.Algebra.Order.Archimedean.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 46 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.
- LinearOrderstatement and proof · cited by 8,572
- Fieldstatement and proof · cited by 7,404
- IsStrictOrderedRingstatement and proof · cited by 2,490
- le_of_ltproof · cited by 1,175
- Archimedeanstatement · cited by 603
- lt_of_le_of_ltproof · cited by 432
- lt_add_oneproof · cited by 105
- Nat.cast_ltproof · cited by 80
- archimedean_iff_nat_ltproof · cited by 5
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