Theorems · Theorem · order theory
div_lt_self
∀ {α : Type u_2} [inst : Semifield α] [inst_1 : PartialOrder α] [PosMulReflectLT α] {a b : α} [IsStrictOrderedRing α],
0 < a → 1 < b → a / b < a- 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
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- PartialOrderstatement and proof · cited by 6,410
- IsStrictOrderedRingstatement and proof · cited by 2,490
- div_oneproof · cited by 629
- zero_lt_oneproof · cited by 598
- Semifieldstatement and proof · cited by 439
- PosMulReflectLTstatement and proof · cited by 278
- div_lt_div_of_pos_leftproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- NumberField.Units.dirichletUnitTheorem.seq_nextproof · cited by 3
- ArithmeticFunction.vonMangoldt.not_summable_residueClass_prime_divproof · cited by 1
- div_nat_lt_self_of_pos_of_two_leproof · cited by 0