Mathlib Map

Theorems · Theorem · order theory

one_div_lt_one_div_of_lt

∀ {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
2 results in Mathlib
Foundations
Depth 46 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
SemifieldPartialOrderPosMulReflectLT
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

lt_of_one_div_lt_one_div · cited by 1lt_of_one_div_lt_one_divNat.one_div_lt_one_div · cited by 0Nat.one_div_lt_one_divPartialOrder · cited by 6410PartialOrderSemifield · cited by 439SemifieldLT.lt.trans · cited by 370lt.transPosMulReflectLT · cited by 278PosMulReflectLTdiv_lt_one · cited by 38div_lt_onelt_div_iff₀' · cited by 16lt_div_iff₀'div_eq_mul_one_div · cited by 10div_eq_mul_one_divone_div_lt_one_div_of_ltCITED BYCITES

Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.