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Theorems · Theorem · order theory

half_le_self_iff

∀ {α : Type u_2} [inst : Semifield α] [inst_1 : PartialOrder α] [PosMulReflectLT α] {a : α} [IsStrictOrderedRing α],
  a / 2 ≤ a ↔ 0 ≤ a
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
Assumes
SemifieldPartialOrderPosMulReflectLTIsStrictOrderedRing
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Around this declaration

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

half_le_self · cited by 5half_le_selfPartialOrder · cited by 6410PartialOrderIsStrictOrderedRing · cited by 2490IsStrictOrderedRingSemifield · cited by 439SemifieldPosMulReflectLT · cited by 278PosMulReflectLTdiv_le_iff₀ · cited by 97div_le_iff₀mul_two · cited by 43mul_twozero_lt_two' · cited by 16zero_lt_two'le_add_iff_nonneg_left · cited by 12le_add_iff_nonneg_lefthalf_le_self_iffCITED BYCITES

Cites8

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Cited by1

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