Theorems · Theorem · order theory
LowerAdjoint.closure_inf_le
∀ {α : Type u_1} {β : Type u_4} [inst : SemilatticeInf α] [inst_1 : Preorder β] {u : β → α} (l : LowerAdjoint u)
(x y : α), u (l.toFun (x ⊓ y)) ≤ u (l.toFun x) ⊓ u (l.toFun y)- Defined in
- Mathlib.Order.Closure
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Quot.sound
- Assumes
- SemilatticeInfPreorder
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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
- SemilatticeInfstatement and proof · cited by 634
- LowerAdjoint.toFunstatement · cited by 105
- LowerAdjointstatement and proof · cited by 38
- LowerAdjoint.closureOperatorproof · cited by 12
- ClosureOperator.closure_inf_leproof · cited by 1
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