Theorems · Theorem · order theory
Finset.mem_Ico
∀ {α : Type u_1} [inst : Preorder α] [inst_1 : LocallyFiniteOrder α] {a b x : α}, x ∈ Finset.Ico a b ↔ a ≤ x ∧ x < b- Defined in
- Mathlib.Order.Interval.Finset.Defs
- Cited by
- 50 results in Mathlib
- Foundations
- Depth 55 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PreorderLocallyFiniteOrder
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.
- Finsetstatement · cited by 13,712
- Preorderstatement and proof · cited by 7,952
- LocallyFiniteOrderstatement and proof · cited by 658
- Finset.Icostatement · cited by 450
- LocallyFiniteOrder.finset_mem_Icoproof · cited by 1
Cited by50
Results whose statement or proof uses this declaration.
- Finset.coe_Icoproof · cited by 66
- Finset.right_notMem_Icoproof · cited by 13
- Finset.sum_eq_sum_Ico_succ_botproof · cited by 8
- IsNilpotent.exp_eq_sumproof · cited by 5
- Finset.Ico_disjoint_Ico_consecutiveproof · cited by 4
- Finset.sum_range_sub_sum_rangeproof · cited by 3
- edist_le_Ico_sum_of_edist_leproof · cited by 3
- MeasureTheory.martingale_martingalePartproof · cited by 2
- dist_le_Ico_sum_of_dist_leproof · cited by 2
- Complex.tendsto_tsum_powerSeries_nhdsWithin_stolzSetproof · cited by 2
- Finset.sum_schlomilch_le'proof · cited by 2
- Real.exists_int_int_abs_mul_sub_leproof · cited by 2