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Theorems · Theorem · order theory

div_nonneg_iff

∀ {α : Type u_2} [inst : Field α] [inst_1 : LinearOrder α] [IsStrictOrderedRing α] {a b : α},
  0 ≤ a / b ↔ 0 ≤ a ∧ 0 ≤ b ∨ a ≤ 0 ∧ b ≤ 0
Defined in
Mathlib.Algebra.Order.Field.Basic
Cited by
3 results in Mathlib
Foundations
Depth 45 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FieldLinearOrderIsStrictOrderedRing
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

strictConvexOn_rpow · cited by 2strictConvexOn_rpowAkraBazziRecurrence.smoothingFn_mul_asympBound_isBigO_T · cited by 1AkraBazziRecurrence.smoot…AkraBazziRecurrence.T_isBigO_smoothingFn_mul_asympBound · cited by 1AkraBazziRecurrence.T_isB…LinearOrder · cited by 8572LinearOrderField · cited by 7404FieldIsStrictOrderedRing · cited by 2490IsStrictOrderedRingdivision_def · cited by 21division_defdiv_nonneg_iffCITED BYCITES

Cites4

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Cited by3

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