Theorems · Theorem · order theory
Set.image_const_sub_Iio
∀ {α : Type u_1} [inst : AddCommGroup α] [inst_1 : PartialOrder α] [IsOrderedAddMonoid α] (a b : α),
(fun x => a - x) '' Set.Iio b = Set.Ioi (a - b)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- AddCommGroupstatement and proof · cited by 12,871
- PartialOrderstatement and proof · cited by 6,410
- Set.imagestatement and proof · cited by 5,609
- Set.preimageproof · cited by 4,946
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- add_commproof · cited by 1,535
- Set.Ioistatement and proof · cited by 1,463
- Set.Iiostatement and proof · cited by 1,166
- sub_eq_add_negproof · cited by 1,023
- neg_negproof · cited by 960
- Set.image_congrproof · cited by 533
Cited by2
Results whose statement or proof uses this declaration.
- Cardinal.mk_Iio_realproof · cited by 1
- Filter.map_subLeft_nhdsLTproof · cited by 0