Theorems · Theorem · order theory
Set.Ioc_subset_Ioi_self
∀ {α : Type u_1} [inst : Preorder α] {a b : α}, Set.Ioc b a ⊆ Set.Ioi b- Defined in
- Mathlib.Order.Interval.Set.Basic
- Cited by
- 24 results in Mathlib
- Foundations
- Depth 11 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.
Cited by24
Results whose statement or proof uses this declaration.
- Fin.image_addNat_Iocproof · cited by 4
- AntitoneOn.sum_Ico_le_integralproof · cited by 3
- intervalIntegral.integral_interval_add_Ioiproof · cited by 3
- Ioi_mem_nhdsSet_Iocproof · cited by 3
- MeasureTheory.lintegral_comp_eq_lintegral_meas_le_mulproof · cited by 3
- Fin.image_natAdd_Iocproof · cited by 3
- Metric.cthickening_eq_iInter_thickeningproof · cited by 3
- Set.Iic_disjoint_Iocproof · cited by 2
- not_differentiableWithinAt_of_deriv_tendsto_atTop_Ioiproof · cited by 2
- StieltjesFunction.measure_Ioi_of_tendsto_atTop_atTopproof · cited by 2
- MeasureTheory.tendsto_limUnder_of_hasDerivAt_of_integrableOn_Ioiproof · cited by 2
- WithBot.image_coe_Iocproof · cited by 2