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Proof step 21 from proof predef_supers-if (previous step)

⊦ class = `java.lang.IndexOutOfBoundsException' .class, class = `java.lang.ArrayStoreException' .class, class = `java.lang.ArithmeticException' .class, class = `java.lang.RuntimeException' .class, class = `java.lang.NoClassDefFoundError' .class, class = `java.lang.Error' .class, class = `*Array*' .class, class = `java.lang.Object' .class, class = `java.lang.Throwable' .class, class = `java.lang.Exception' .class, class = `java.lang.ExceptionInInitializerError' .class, class = `java.lang.NullPointerException' .class, class = `java.lang.ClassCastException' .class, class = `java.lang.NegativeArraySizeException' .class, predef_supers(class) = ((class = `java.lang.ArrayIndexOutOfBoundsException' .class ⊃ `java.lang.ArrayIndexOutOfBoundsException' .class ' + `java.lang.IndexOutOfBoundsException' .class ' + `java.lang.RuntimeException' .class ' + `java.lang.Exception' .class ' + `java.lang.Throwable' .class ' + `java.lang.Object' .class ' ; [] ) )

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 15:
⊦ ¬ is_predefined_class(class) → predef_supers(class) = []
Proof step 19:
¬ ¬ is_predefined_class(class) ⊦ class = `java.lang.IndexOutOfBoundsException' .class, class = `java.lang.ArrayStoreException' .class, class = `java.lang.ArithmeticException' .class, class = `java.lang.RuntimeException' .class, class = `java.lang.NoClassDefFoundError' .class, class = `java.lang.Error' .class, class = `*Array*' .class, class = `java.lang.Object' .class, class = `java.lang.Throwable' .class, class = `java.lang.Exception' .class, class = `java.lang.ExceptionInInitializerError' .class, class = `java.lang.NullPointerException' .class, class = `java.lang.ClassCastException' .class, class = `java.lang.NegativeArraySizeException' .class, predef_supers(class) = ((class = `java.lang.ArrayIndexOutOfBoundsException' .class ⊃ `java.lang.ArrayIndexOutOfBoundsException' .class ' + `java.lang.IndexOutOfBoundsException' .class ' + `java.lang.RuntimeException' .class ' + `java.lang.Exception' .class ' + `java.lang.Throwable' .class ' + `java.lang.Object' .class ' ; [] ) )
Proof step 20:
⊦ is_predefined_class(`java.lang.ArrayIndexOutOfBoundsException' .class)

Rule argument

[x0lemmaarg: spec-name: predefined instance-name: lemma-name: supers-not antecedent: succedent: ¬ is_predefined_class(class) → predef_supers(class) = [] substlist: [class] → [class] add preconditions?: F is rewrite lemma?: T current spec?: T rotate lemma?: F replace all?: T paths: () dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : list, classnames, e-01, ⊦ class ' + classes ≠ []], [CSIMPNAMEDSEQ : list, classnames, a, ⊦ (classes + classes0) + classes1 = classes + classes0 + classes1], [CSIMPNAMEDSEQ : classname, , inj, ⊦ stringvar .class = stringvar0 .class ↔ stringvar = stringvar0])], [EXTRATERMS : (class)]]