Theorems · Theorem · order theory
Set.Icc_sdiff_left
∀ {α : Type u_1} [inst : PartialOrder α] {a b : α}, Set.Icc a b \ {a} = Set.Ioc a b- Defined in
- Mathlib.Order.Interval.Set.Basic
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses propext, Quot.sound
- Assumes
- PartialOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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.extproof · cited by 2,266
- Set.Iccstatement · cited by 1,702
- Set.Iocstatement · cited by 971
Cited by8
Results whose statement or proof uses this declaration.
- Set.Icc_sdiff_bothproof · cited by 4
- Set.image_update_Iocproof · cited by 4
- Set.Ioc_union_leftproof · cited by 3
- Finset.Icc_erase_leftproof · cited by 1
- Set.mem_Icc_Ico_Ioc_Ioo_of_subset_of_subsetproof · cited by 1
- Set.Icc_sdiff_Ioc_sameproof · cited by 1
- WCovBy.Ioc_subsetproof · cited by 0
- Set.Icc_diff_leftproof · cited by 0