Theorems · Theorem · order theory
one_div_le_one_div_of_le
∀ {α : Type u_2} [inst : Semifield α] [inst_1 : PartialOrder α] [PosMulReflectLT α] {a b : α},
0 < a → a ≤ b → 1 / b ≤ 1 / a- Defined in
- Mathlib.Algebra.Order.Field.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 45 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- one_divproof · cited by 624
- Semifieldstatement and proof · cited by 439
- PosMulReflectLTstatement and proof · cited by 278
- inv_anti₀proof · cited by 27
Cited by5
Results whose statement or proof uses this declaration.
- setOfPred_liouvilleWith_subset_auxproof · cited by 2
- Nat.one_div_le_one_divproof · cited by 1
- le_of_one_div_le_one_divproof · cited by 0
- ProbabilityTheory.IsPreBrownianReal.invproof · cited by 0
- GenContFract.abs_sub_convergents_le'proof · cited by 0