Theorems · Theorem · order theory
Set.preimage_mul_const_Iio
∀ {α : Type u_1} [inst : CommGroup α] [inst_1 : PartialOrder α] [IsOrderedMonoid α] (a b : α),
(fun x => x * a) ⁻¹' Set.Iio b = Set.Iio (b / a)- Cited by
- 9 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- PartialOrderstatement and proof · cited by 6,410
- Set.preimagestatement · cited by 4,946
- Set.extproof · cited by 2,266
- Set.Iiostatement · cited by 1,166
- CommGroupstatement and proof · cited by 990
- IsOrderedMonoidstatement and proof · cited by 577
- lt_div_iff_mul_ltproof · cited by 4
Cited by9
Results whose statement or proof uses this declaration.
- Set.preimage_mul_const_Iooproof · cited by 3
- Set.preimage_mul_const_Icoproof · cited by 3
- Set.image_const_div_Ioiproof · cited by 1
- Set.image_mul_const_Iioproof · cited by 1
- Set.image_div_const_Iioproof · cited by 1
- Set.image_const_mul_Iioproof · cited by 0
- Set.preimage_div_const_Iioproof · cited by 0
- Filter.map_mul_left_nhdsLTproof · cited by 0
- Filter.map_mul_right_nhdsLTproof · cited by 0