Theorems · Definition · order theory
Set.Icc
{α : Type u_1} → [Preorder α] → α → α → Set αIcc a b is the left-closed right-closed interval $[a, b]$.
- Defined in
- Mathlib.Order.Interval.Set.Defs
- Cited by
- 1,702 results in Mathlib
- Foundations
- Depth 2 from the axioms, rests on 8 definitions · uses no axioms
- Assumes
- Preorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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.ofPredproof · cited by 6,101
Cited by1,786
Results whose statement or proof uses this declaration.
- unitIntervalproof · cited by 607
- Set.uIccproof · cited by 393
- BoxIntegral.Box.Iccproof · cited by 76
- Set.left_mem_Iccstatement · cited by 67
- Set.Icc_selfstatement · cited by 63
- Set.right_mem_Iccstatement · cited by 60
- Finset.coe_Iccstatement · cited by 60
- Set.projIccstatement · cited by 56
- Set.uIcc_of_lestatement and proof · cited by 54
- Set.Ioo_subset_Icc_selfstatement · cited by 54
- Set.Ioc_subset_Icc_selfstatement · cited by 53
- Set.OrdConnected.outstatement · cited by 47
Showing the 200 most cited of 1,786.