Theorems · Theorem · order theory
div_nat_le_self_of_nonnneg
∀ {α : Type u_2} [inst : Semifield α] [inst_1 : PartialOrder α] [PosMulReflectLT α] {a : α} [IsStrictOrderedRing α],
0 ≤ a → ∀ (n : ℕ), a / ↑n ≤ a- Defined in
- Mathlib.Algebra.Order.Field.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 46 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- PartialOrderstatement and proof · cited by 6,410
- IsStrictOrderedRingstatement and proof · cited by 2,490
- Nat.cast_zeroproof · cited by 1,870
- Semifieldstatement and proof · cited by 439
- PosMulReflectLTstatement and proof · cited by 278
- div_zeroproof · cited by 251
- div_le_selfproof · cited by 12
- Nat.one_le_cast_iff_ne_zeroproof · cited by 1
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