Theorems · Theorem · order theory
Set.Finite.infClosure
∀ {α : Type u_3} [inst : SemilatticeInf α] {s : Set α}, s.Finite → (infClosure s).FiniteThe semilattice generated by a finite set is finite.
- Defined in
- Mathlib.Order.SupClosed
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemilatticeInf
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Finsetproof · cited by 13,712
- SetLike.coeproof · cited by 8,199
- Set.Finitestatement and proof · cited by 1,814
- Finset.Nonemptyproof · cited by 1,001
- Finset.filterproof · cited by 949
- Finset.imageproof · cited by 910
- SemilatticeInfstatement and proof · cited by 634
- ClosureOperatorstatement · cited by 371
- Set.Finite.subsetproof · cited by 285
- Finset.coe_imageproof · cited by 222
Cited by1
Results whose statement or proof uses this declaration.
- Set.Finite.latticeClosureproof · cited by 1