Theorems · Theorem · order theory
Set.Ioc_sdiff_Ioo_same
∀ {α : Type u_1} [inst : PartialOrder α] {a b : α}, b < a → Set.Ioc b a \ Set.Ioo b a = {a}- Defined in
- Mathlib.Order.Interval.Set.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 58 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PartialOrder
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 and proof · cited by 53,352
- PartialOrderstatement and proof · cited by 6,410
- Set.Ioostatement · cited by 1,214
- Set.Iocstatement and proof · cited by 971
- Set.singleton_subset_iffproof · cited by 206
- Set.sdiff_sdiff_cancel_leftproof · cited by 21
- Set.right_mem_Iocproof · cited by 18
- Set.Ioc_sdiff_rightproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- Finset.Ioc_sdiff_Ioo_selfproof · cited by 1