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Proof step 5 from proof in-predefs (conclusion)

⊦ class ∈ predefined_classes ↔ is_predefined_class(class)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
⊦ predefined_classes = `java.lang.NullPointerException' .class + `java.lang.ArithmeticException' .class + `java.lang.ClassCastException' .class + `java.lang.ArrayStoreException' .class + `java.lang.NegativeArraySizeException' .class + `java.lang.ArrayIndexOutOfBoundsException' .class + `java.lang.IndexOutOfBoundsException' .class + `java.lang.RuntimeException' .class + `java.lang.NoClassDefFoundError' .class + `java.lang.ExceptionInInitializerError' .class + `java.lang.Error' .class + `java.lang.Exception' .class + `java.lang.Throwable' .class + (`*Array*' .class + `java.lang.Object' .class)
Proof step 4:
⊦ class ∈ `java.lang.NullPointerException' .class + `java.lang.ArithmeticException' .class + `java.lang.ClassCastException' .class + `java.lang.ArrayStoreException' .class + `java.lang.NegativeArraySizeException' .class + `java.lang.ArrayIndexOutOfBoundsException' .class + `java.lang.IndexOutOfBoundsException' .class + `java.lang.RuntimeException' .class + `java.lang.NoClassDefFoundError' .class + `java.lang.ExceptionInInitializerError' .class + `java.lang.Error' .class + `java.lang.Exception' .class + `java.lang.Throwable' .class + (`*Array*' .class + `java.lang.Object' .class) ↔ is_predefined_class(class)

Rule argument

[x0lemmaarg: spec-name: predefined instance-name: lemma-name: predef-classes antecedent: succedent: predefined_classes = `java.lang.NullPointerException' .class + `java.lang.ArithmeticException' .class + `java.lang.ClassCastException' .class + `java.lang.ArrayStoreException' .class + `java.lang.NegativeArraySizeException' .class + `java.lang.ArrayIndexOutOfBoundsException' .class + `java.lang.IndexOutOfBoundsException' .class + `java.lang.RuntimeException' .class + `java.lang.NoClassDefFoundError' .class + `java.lang.ExceptionInInitializerError' .class + `java.lang.Error' .class + `java.lang.Exception' .class + `java.lang.Throwable' .class + (`*Array*' .class + `java.lang.Object' .class) substlist: [] → [] add preconditions?: F is rewrite lemma?: T current spec?: T rotate lemma?: F replace all?: T paths: () dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : ()]]