Theorems · Theorem · order theory
Set.Ici_subset_Ioi
∀ {α : Type u_1} [inst : Preorder α] {a b : α}, Set.Ici a ⊆ Set.Ioi b ↔ b < a- Defined in
- Mathlib.Order.Interval.Set.Basic
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses propext
- Assumes
- Preorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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.Ioistatement and proof · cited by 1,463
- Set.Icistatement and proof · cited by 1,070
- Set.self_mem_Iciproof · cited by 30
- lt_of_le_of_lt'proof · cited by 11
Cited by15
Results whose statement or proof uses this declaration.
- Filter.atTop_basis_Ioiproof · cited by 10
- borel_eq_generateFrom_Iioproof · cited by 6
- WithBot.image_coe_Icoproof · cited by 3
- MeasureTheory.tendsto_limUnder_of_hasDerivAt_of_integrableOn_Ioiproof · cited by 2
- WithBot.image_coe_Iccproof · cited by 2
- Ioi_mem_nhdsSet_Ici_iffproof · cited by 2
- IsGLB.biUnion_Ici_eq_Ioiproof · cited by 2
- Filter.map_val_Ioi_atTopproof · cited by 2
- Filter.atTop_Ioi_eqproof · cited by 1
- WithBot.image_coe_Iciproof · cited by 1
- nhdsGE_eq_iInf_inf_principalproof · cited by 1
- Set.image_subtype_val_Ioi_Iciproof · cited by 1