Theorems · Theorem · order theory
Finset.mem_Icc
∀ {α : Type u_1} [inst : Preorder α] [inst_1 : LocallyFiniteOrder α] {a b x : α}, x ∈ Finset.Icc a b ↔ a ≤ x ∧ x ≤ b- Defined in
- Mathlib.Order.Interval.Finset.Defs
- Cited by
- 39 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.Iccstatement · cited by 348
- LocallyFiniteOrder.finset_mem_Iccproof · cited by 1
Cited by39
Results whose statement or proof uses this declaration.
- Finset.coe_Iccproof · cited by 60
- Finset.mem_uIccproof · cited by 4
- IncidenceAlgebra.mu_mul_zetaproof · cited by 3
- IncidenceAlgebra.mu_toDualproof · cited by 3
- Finset.left_mem_uIccproof · cited by 3
- nivenproof · cited by 2
- Nat.primeFactors_lcmUptoproof · cited by 2
- Finset.right_mem_uIccproof · cited by 2
- LSeriesSummable_of_sum_norm_bigOproof · cited by 2
- Chebyshev.psi_eq_sum_theta'proof · cited by 2
- Real.exists_int_int_abs_mul_sub_leproof · cited by 2
- setOfPred_liouvilleWith_subset_auxproof · cited by 2