Theorems · Theorem · order theory
Set.self_mem_Ici
∀ {α : Type u_1} [inst : Preorder α] {a : α}, a ∈ Set.Ici a- Defined in
- Mathlib.Order.Interval.Set.Basic
- Cited by
- 30 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses propext
- 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.Icistatement · cited by 1,070
- Set.mem_Iciproof · cited by 37
- Std.ge_reflproof · cited by 23
Cited by30
Results whose statement or proof uses this declaration.
- Set.Iic_subset_Iicproof · cited by 25
- Set.Ici_subset_Ioiproof · cited by 15
- Set.nonempty_Iciproof · cited by 9
- MeasureTheory.integral_Ioi_of_hasDerivAt_of_tendsto'proof · cited by 7
- isLeast_Iciproof · cited by 7
- MeasureTheory.integrableOn_Ioi_deriv_of_nonneg'proof · cited by 4
- Set.Ici_sdiff_Ioi_sameproof · cited by 4
- Filter.eventuallyConst_atTopproof · cited by 3
- StrictMonoOn.continuousWithinAt_right_of_exists_betweenproof · cited by 3
- IsMin.Iic_eqproof · cited by 3
- continuousWithinAt_right_of_monotoneOn_of_exists_betweenproof · cited by 3
- Filter.Subsingleton.atTop_eqproof · cited by 3