Theorems · Theorem · order theory
div_le_one_of_ge
∀ {α : Type u_2} [inst : Field α] [inst_1 : PartialOrder α] [PosMulReflectLT α] [IsStrictOrderedRing α] {a b : α},
b ≤ a → b ≤ 0 → a / b ≤ 1- Defined in
- Mathlib.Algebra.Order.Field.Basic
- Cited by
- 1 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.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fieldstatement and proof · cited by 7,404
- PartialOrderstatement and proof · cited by 6,410
- IsStrictOrderedRingstatement and proof · cited by 2,490
- PosMulReflectLTstatement and proof · cited by 278
- neg_le_negproof · cited by 34
- div_le_one_of_le₀proof · cited by 31
- neg_div_neg_eqproof · cited by 17
- neg_nonneg_of_nonposproof · cited by 9
Cited by1
Results whose statement or proof uses this declaration.
- parallelepiped_singleproof · cited by 1