Theorems · Theorem · order theory
Set.inv_Ioc
∀ {α : Type u_1} [inst : CommGroup α] [inst_1 : PartialOrder α] [IsOrderedMonoid α] (a b : α),
(Set.Ioc a b)⁻¹ = Set.Ico b⁻¹ a⁻¹- Cited by
- 2 results in Mathlib
- Foundations
- Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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.Ioiproof · cited by 1,463
- Set.Iioproof · cited by 1,166
- Set.Iicproof · cited by 1,111
- Set.Iciproof · cited by 1,070
- CommGroupstatement and proof · cited by 990
- Set.Iocstatement · cited by 971
- Set.Icostatement · cited by 799
- IsOrderedMonoidstatement and proof · cited by 577
- Set.inter_commproof · cited by 291
- Set.invstatement · cited by 132
Cited by2
Results whose statement or proof uses this declaration.
- Set.image_inv_Iocproof · cited by 0
- Set.image_const_div_Iocproof · cited by 0