Theorems · Theorem · order theory
div_le_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
- 12 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_le_div_of_nonneg_leftproof · cited by 6
Cited by12
Results whose statement or proof uses this declaration.
- Real.sin_pi_over_two_pow_succproof · cited by 6
- Real.lt_tanproof · cited by 2
- AddCircle.ae_empty_or_univ_of_forall_vadd_ae_eq_selfproof · cited by 2
- Circle.mem_centeredArc_divproof · cited by 1
- AddCircle.isAddFundamentalDomain_of_ae_ballproof · cited by 1
- Int.ceil_div_ceil_inv_sub_oneproof · cited by 1
- Nat.ceil_le_mulproof · cited by 1
- AddCircle.exists_norm_nsmul_leproof · cited by 0
- hoferproof · cited by 0
- Circle.eq_one_of_forall_pow_mem_centeredArc_pi_div_twoproof · cited by 0
- Real.arcsin_eq_arccosproof · cited by 0
- div_nat_le_self_of_nonnnegproof · cited by 0