Theorems · Theorem · order theory
Set.mem_Icc_of_Ico
∀ {α : Type u_1} [inst : Preorder α] {a b x : α}, x ∈ Set.Ico b a → x ∈ Set.Icc b a- Defined in
- Mathlib.Order.Interval.Set.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses propext, Quot.sound
- Assumes
- Preorder
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
- Preorderstatement and proof · cited by 7,952
- Set.Iccstatement · cited by 1,702
- Set.Icostatement and proof · cited by 799
- Set.Ico_subset_Icc_selfproof · cited by 41
Cited by4
Results whose statement or proof uses this declaration.
- Real.arcsin_le_iff_le_sin'proof · cited by 3
- Function.Periodic.integral_le_sSup_add_zsmul_of_posproof · cited by 1
- Function.Periodic.sInf_add_zsmul_le_integral_of_posproof · cited by 1
- eq_of_derivWithin_eqproof · cited by 0