Theorems · Theorem · order theory
Set.Ioo_insert_left
∀ {α : Type u_1} [inst : PartialOrder α] {a b : α}, a < b → insert a (Set.Ioo a b) = Set.Ico a b- Defined in
- Mathlib.Order.Interval.Set.Basic
- Cited by
- 4 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.
Cites7
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 and proof · cited by 1,214
- Set.Icostatement and proof · cited by 799
- Set.union_commproof · cited by 99
- Set.insert_eqproof · cited by 47
- Set.Ioo_union_leftproof · cited by 4
Cited by4
Results whose statement or proof uses this declaration.
- CFC.monotone_nnrpowproof · cited by 3
- CFC.concaveOn_nnrpowproof · cited by 2
- Set.insert_Ico_succ_left_eq_Icoproof · cited by 2
- nhdsSet_Icoproof · cited by 0