Theorems · Definition · order theory
Finset.Icc
{α : Type u_1} → [inst : Preorder α] → [LocallyFiniteOrder α] → α → α → Finset αThe finset $[a, b]$ of elements x such that a ≤ x and x ≤ b. Basically Set.Icc a b as a
finset.
- Defined in
- Mathlib.Order.Interval.Finset.Defs
- Cited by
- 348 results in Mathlib
- Foundations
- Depth 3 from the axioms, rests on 5 definitions · uses no axioms
- Assumes
- PreorderLocallyFiniteOrder
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.
- Finsetstatement · cited by 13,712
- Preorderstatement and proof · cited by 7,952
- LocallyFiniteOrderstatement and proof · cited by 658
- LocallyFiniteOrder.finsetIccproof · cited by 1
Cited by359
Results whose statement or proof uses this declaration.
- Finset.uIccproof · cited by 84
- Nat.divisorsAntidiagonalproof · cited by 61
- Finset.coe_Iccstatement · cited by 60
- Finset.mem_Iccstatement · cited by 39
- SummationFilter.symmetricIccproof · cited by 16
- Nat.card_Iccstatement · cited by 14
- Multiset.Iccproof · cited by 14
- SummationFilter.conditionalproof · cited by 13
- Nat.lcmUptoproof · cited by 13
- Finset.boxproof · cited by 12
- Finset.Icc_selfstatement · cited by 12
- Nat.mem_divisorsAntidiagonalproof · cited by 11
Showing the 200 most cited of 359.