Theorems · Theorem · order theory
div_le_div_of_nonneg_left
∀ {G₀ : Type u_3} [inst : GroupWithZero G₀] [inst_1 : PartialOrder G₀] [PosMulReflectLT G₀] [MulPosReflectLT G₀]
{a b c : G₀}, 0 ≤ a → 0 < c → c ≤ b → a / b ≤ a / c- Cited by
- 6 results in Mathlib
- Foundations
- Depth 25 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
- div_eq_mul_invproof · cited by 715
- GroupWithZerostatement and proof · cited by 691
- mul_le_mul_of_nonneg_leftproof · cited by 361
- PosMulReflectLTstatement and proof · cited by 278
- MulPosReflectLTstatement and proof · cited by 93
- inv_anti₀proof · cited by 27
Cited by6
Results whose statement or proof uses this declaration.
- div_le_selfproof · cited by 12
- GenContFract.abs_sub_convs_leproof · cited by 2
- PadicInt.fwdDiff_iter_le_of_forall_leproof · cited by 1
- le_div_selfproof · cited by 1
- ArithmeticFunction.vonMangoldt.not_summable_residueClass_prime_divproof · cited by 1
- Behrend.exists_large_sphereproof · cited by 1