Theorems · Theorem · order theory
Set.Icc_sdiff_both
∀ {α : Type u_1} [inst : PartialOrder α] {a b : α}, Set.Icc a b \ {a, b} = Set.Ioo a b- Defined in
- Mathlib.Order.Interval.Set.Basic
- Cited by
- 4 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.Iccstatement and proof · cited by 1,702
- Set.Ioostatement and proof · cited by 1,214
- Set.insert_eqproof · cited by 47
- Set.sdiff_sdiffproof · cited by 10
- Set.Icc_sdiff_leftproof · cited by 8
- Set.Ioc_sdiff_rightproof · cited by 5
Cited by4
Results whose statement or proof uses this declaration.
- Set.Icc_sdiff_Ioo_sameproof · cited by 7
- Finset.Icc_sdiff_bothproof · cited by 1
- Set.Icc_diff_bothproof · cited by 0
- Set.Ioo_union_bothproof · cited by 0