Theorems · Theorem · order theory
Set.Icc_sdiff_Ioo_same
∀ {α : Type u_1} [inst : PartialOrder α] {a b : α}, a ≤ b → Set.Icc a b \ Set.Ioo a b = {a, b}- Defined in
- Mathlib.Order.Interval.Set.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 59 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.
Cites6
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 · cited by 1,214
- Set.sdiff_sdiff_cancel_leftproof · cited by 21
- Set.Icc_sdiff_bothproof · cited by 4
Cited by7
Results whose statement or proof uses this declaration.
- closure_Iooproof · cited by 20
- Finset.Icc_sdiff_Ioo_selfproof · cited by 1
- frontier_Iooproof · cited by 1
- frontier_Iocproof · cited by 0
- frontier_Iccproof · cited by 0
- Set.Icc_diff_Ioo_sameproof · cited by 0
- frontier_Icoproof · cited by 0