Theorems · Theorem · order theory
Finset.left_notMem_Ioc
∀ {α : Type u_2} {a b : α} [inst : Preorder α] [inst_1 : LocallyFiniteOrder α], a ∉ Finset.Ioc a b- Defined in
- Mathlib.Order.Interval.Finset.Basic
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 56 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.
Cites6
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.Iocstatement and proof · cited by 301
- lt_irreflproof · cited by 190
- Finset.mem_Iocproof · cited by 26
Cited by8
Results whose statement or proof uses this declaration.
- Finset.Icc_eq_cons_Iocstatement and proof · cited by 6
- Finset.add_sum_Ioc_eq_sum_Iccproof · cited by 5
- sum_mul_eq_sub_integral_mulproof · cited by 1
- sum_mul_eq_sub_integral_mul₀proof · cited by 1
- Finset.mul_prod_Ioc_eq_prod_Iccproof · cited by 1
- Multiset.left_notMem_Iocproof · cited by 0
- Polynomial.coeff_divByMonic_X_sub_Cproof · cited by 0
- summable_mul_of_bigO_atTop'proof · cited by 0