取自课堂讲稿的Isabelle函数定义中的错误

为什么函数（类）的以下定义

定义不减损：：“实数集=>（实数=>实数）=>bool”

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其中“在SF上不减损”（所有x:S.所有y:S.x f x您可以在Isabelle/jEdit中看到

definition nondecreasing_on :: "real set => (real => real) => bool"
where "nondecreasing_on S f <-> (ALL x:S. ALL y:S. x<=y --> f x <= f y)"

definition nondecreasing_on :: "real set ⇒ (real ⇒ real) ⇒ bool"
  where "nondecreasing_on S f ⟷ (∀x∈S. ∀y∈S. x ≤ y ⟶ f x ≤ f y)"