Theorems · Theorem · order theory
Set.right_mem_Icc
∀ {α : Type u_1} [inst : Preorder α] {a b : α}, a ∈ Set.Icc b a ↔ b ≤ a- Defined in
- Mathlib.Order.Interval.Set.Basic
- Cited by
- 60 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.
Cites4
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
- Std.ge_reflproof · cited by 23
Cited by62
Results whose statement or proof uses this declaration.
- Real.arcsin_of_one_leproof · cited by 7
- Real.arcsin_oneproof · cited by 6
- intervalIntegral.continuousWithinAt_primitiveproof · cited by 6
- Set.projIcc_of_right_lestatement and proof · cited by 5
- isGreatest_Iccproof · cited by 4
- intermediate_value_Iccproof · cited by 4
- Set.IccExtend_of_right_lestatement · cited by 4
- MonotoneOn.mapsTo_Iccproof · cited by 3
- Set.Ico_union_rightproof · cited by 3
- intermediate_value_Icc'proof · cited by 3
- PhragmenLindelof.horizontal_stripproof · cited by 3
- AntitoneOn.mapsTo_Iccproof · cited by 3