Theorems · Theorem · order theory
Set.Ico_eq_empty
∀ {α : Type u_1} [inst : Preorder α] {a b : α}, ¬a < b → Set.Ico a b = ∅- Defined in
- Mathlib.Order.Interval.Set.Basic
- Cited by
- 24 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Quot.sound
- 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.Icostatement and proof · cited by 799
- LE.le.trans_ltproof · cited by 795
- Set.eq_empty_iff_forall_notMemproof · cited by 42
Cited by24
Results whose statement or proof uses this declaration.
- intervalIntegral.sum_integral_adjacent_intervals_Icoproof · cited by 4
- Set.Ico_succ_left_eq_Iooproof · cited by 4
- IntervalIntegrable.trans_iterate_Icoproof · cited by 3
- Set.Icc_eq_Ico_same_iffproof · cited by 2
- StieltjesFunction.measure_Icoproof · cited by 2
- integrableOn_Icc_iff_integrableOn_Ico'proof · cited by 1
- integrableOn_Ico_iff_integrableOn_Ioo'proof · cited by 1
- Set.Ioo_eq_Ico_same_iffproof · cited by 1
- Continuous.image_Ico_of_strictMonoproof · cited by 1
- Set.Ico_eq_empty_of_leproof · cited by 1
- Polynomial.Chebyshev.T_derivative_mem_span_Tproof · cited by 1
- isClosed_Ico_iffproof · cited by 1