Theorems · Theorem · order theory
Set.Ici_sdiff_Ioi_same
∀ {α : Type u_1} [inst : PartialOrder α] {a : α}, Set.Ici a \ Set.Ioi a = {a}- 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.Ioistatement · cited by 1,463
- Set.Icistatement and proof · cited by 1,070
- Set.singleton_subset_iffproof · cited by 206
- Set.self_mem_Iciproof · cited by 30
- Set.sdiff_sdiff_cancel_leftproof · cited by 21
- Set.Ici_sdiff_leftproof · cited by 6
Cited by4
Results whose statement or proof uses this declaration.
- closure_Ioi'proof · cited by 5
- not_differentiableWithinAt_of_deriv_tendsto_atTop_Ioiproof · cited by 2
- frontier_Ici'proof · cited by 1
- frontier_Ioi'proof · cited by 1