Mathlib Map

Theorems · Theorem · order theory

ClosureOperator.sInf_isClosed

∀ {α : Type u_1} [inst : CompleteLattice α] {c : ClosureOperator α} {S : Set α},
  (∀ x ∈ S, c.IsClosed x) → c.IsClosed (sInf S)
Defined in
Mathlib.Order.Closure
Cited by
0 results in Mathlib
Foundations
Depth 16 from the axioms · uses propext, Quot.sound
Assumes
CompleteLattice
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Set · cited by 53352SetCompleteLattice · cited by 1048CompleteLatticeInfSet.sInf · cited by 935InfSet.sInfClosureOperator · cited by 371ClosureOperatorClosureOperator.IsClosed · cited by 38ClosureOperator.IsClosedsInf_eq_iInf · cited by 22sInf_eq_iInfClosureOperator.monotone · cited by 18ClosureOperator.monotoneClosureOperator.isClosed_iff · cited by 14ClosureOperator.isClosed_…Monotone.map_sInf_le · cited by 4Monotone.map_sInf_leClosureOperator.isClosed_iff_closure_le · cited by 3ClosureOperator.isClosed_…biInf_congr · cited by 2biInf_congrClosureOperator.sInf_isClosedCITED BYCITES

Cites11

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by0

Results whose statement or proof uses this declaration.

Nothing cites this yet.