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Theorems · Theorem · order theory

left_lt_add_div_two

∀ {α : Type u_2} [inst : Semifield α] [inst_1 : PartialOrder α] [PosMulReflectLT α] {a b : α} [IsStrictOrderedRing α],
  a < (a + b) / 2 ↔ a < b
Defined in
Mathlib.Algebra.Order.Field.Basic
Cited by
2 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.

BoxIntegral.Box.mem_splitCenterBox · cited by 3Box.mem_splitCenterBoxBoundedContinuousFunction.exists_extension_forall_exists_le_ge_of_isClosedEmbedding · cited by 1BoundedContinuousFunction…PartialOrder · cited by 6410PartialOrderIsStrictOrderedRing · cited by 2490IsStrictOrderedRingSemifield · cited by 439SemifieldPosMulReflectLT · cited by 278PosMulReflectLTmul_two · cited by 43mul_twoleft_lt_add_div_twoCITED BYCITES

Cites5

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Cited by2

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