A boggy definition of Infinity

Consider the following type:

Set Implicit Arguments.

CoInductive LList (A:Set) : Set :=
  | LNil : LList A
  | LCons : A -> LList A -> LList A.

Implicit Arguments LNil [A].

A distracted student confuses keywords and gives an inductive definition of being infinite:

Inductive BugInfinite (A:Set) : LList A -> Prop :=
    BugInfinite_intro :
      forall a (l:LList A),
        BugInfinite l -> BugInfinite (LCons a l).

Show that this predicate can never be satisfied.

Solution

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Pierre Castéran