Theorems · Theorem · order theory
Set.Ico_insert_right
∀ {α : Type u_1} [inst : PartialOrder α] {a b : α}, a ≤ b → insert b (Set.Ico a b) = Set.Icc a b- Defined in
- Mathlib.Order.Interval.Set.Basic
- Cited by
- 5 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.Iccstatement and proof · cited by 1,702
- Set.Icostatement and proof · cited by 799
- Set.union_commproof · cited by 99
- Set.insert_eqproof · cited by 47
- Set.Ico_union_rightproof · cited by 3
Cited by5
Results whose statement or proof uses this declaration.
- Set.insert_Ico_right_eq_Ico_succ_of_not_isMaxproof · cited by 3
- CFC.monotone_nnrpowproof · cited by 3
- CFC.concaveOn_nnrpowproof · cited by 2
- Set.insert_Ico_pred_right_eq_Icoproof · cited by 2
- hasSum_one_div_pow_mul_fourier_mul_bernoulliFunproof · cited by 1