Theorems · Theorem · order theory
Set.neg_Iio
∀ {α : Type u_1} [inst : AddCommGroup α] [inst_1 : PartialOrder α] [IsOrderedAddMonoid α] (a : α),
-Set.Iio a = Set.Ioi (-a)- Cited by
- 8 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.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- AddCommGroupstatement and proof · cited by 12,871
- PartialOrderstatement and proof · cited by 6,410
- Set.extproof · cited by 2,266
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- Set.Ioistatement · cited by 1,463
- Set.Iiostatement · cited by 1,166
- Set.negstatement · cited by 168
- neg_ltproof · cited by 21
Cited by8
Results whose statement or proof uses this declaration.
- Set.neg_Iooproof · cited by 4
- integrable_rpow_mul_exp_neg_mul_sqproof · cited by 2
- Set.image_const_sub_Iioproof · cited by 2
- HasDerivAt.lhopital_zero_atBot_on_Iioproof · cited by 2
- Set.neg_Icoproof · cited by 2
- MeasureTheory.IntegrableOn.comp_neg_Ioiproof · cited by 0
- Filter.neg_nhdsLTproof · cited by 0
- Set.image_neg_Iioproof · cited by 0