Theorems · Theorem · order theory
LowerAdjoint.closure_sup_closure_left
∀ {α : Type u_1} {β : Type u_4} [inst : SemilatticeSup α] [inst_1 : Preorder β] {u : β → α} (l : LowerAdjoint u)
(x y : α), u (l.toFun (u (l.toFun x) ⊔ y)) = u (l.toFun (x ⊔ y))- Defined in
- Mathlib.Order.Closure
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Quot.sound
- Assumes
- SemilatticeSupPreorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- SemilatticeSupstatement and proof · cited by 785
- LowerAdjoint.toFunstatement · cited by 105
- LowerAdjointstatement and proof · cited by 38
- LowerAdjoint.closureOperatorproof · cited by 12
- ClosureOperator.closure_sup_closure_leftproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- LowerAdjoint.closure_union_closure_leftproof · cited by 1