Theorems · Theorem · order theory
isUpperSet_Ici
∀ {α : Type u_1} [inst : Preorder α] (a : α), IsUpperSet (Set.Ici a)- Defined in
- Mathlib.Order.UpperLower.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses no axioms
- Assumes
- Preorder
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.
- Preorderstatement and proof · cited by 7,952
- Set.Icistatement · cited by 1,070
- IsUpperSetstatement · cited by 148
- ge_transproof · cited by 34
Cited by6
Results whose statement or proof uses this declaration.
- UpperSet.Iciproof · cited by 38
- Topology.IsLower.isLowerSet_of_isOpenproof · cited by 4
- MvPolynomial.idealOfVars_eq_restrictSupportIdealstatement and proof · cited by 1
- MvPolynomial.pow_idealOfVarsstatement and proof · cited by 1
- not_bddAbove_Iciproof · cited by 1
- MvPolynomial.mem_pow_idealOfVars_iffproof · cited by 0