Theorems · Theorem · combinatorics
lowerClosure_infs
∀ {α : Type u_2} [inst : SemilatticeInf α] (s t : Set α), lowerClosure (s ⊼ t) = lowerClosure s ⊓ lowerClosure t- Defined in
- Mathlib.Data.Set.Sups
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext, Quot.sound
- Assumes
- SemilatticeInf
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- SetLike.coeproof · cited by 8,199
- LE.le.transproof · cited by 3,151
- Set.extproof · cited by 2,266
- SemilatticeInfstatement and proof · cited by 634
- inf_le_leftproof · cited by 286
- inf_le_rightproof · cited by 238
- LowerSetstatement · cited by 230
- le_infproof · cited by 107
- HasInfs.infsstatement · cited by 105
- lowerClosurestatement and proof · cited by 83
- Set.hasInfsstatement · cited by 43
Cited by1
Results whose statement or proof uses this declaration.
- Finset.truncatedSup_infs_of_notMemproof · cited by 1