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Proof step 18 from proof predef_supers-if (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 16:
⊦ is_predefined_class(class) ↔ class = `java.lang.Object' .class ∨ class = `*Array*' .class ∨ class = `java.lang.NullPointerException' .class ∨ class = `java.lang.ArithmeticException' .class ∨ class = `java.lang.ClassCastException' .class ∨ class = `java.lang.ArrayStoreException' .class ∨ class = `java.lang.NegativeArraySizeException' .class ∨ class = `java.lang.ArrayIndexOutOfBoundsException' .class ∨ class = `java.lang.IndexOutOfBoundsException' .class ∨ class = `java.lang.NoClassDefFoundError' .class ∨ class = `java.lang.ExceptionInInitializerError' .class ∨ class = `java.lang.Error' .class ∨ class = `java.lang.RuntimeException' .class ∨ class = `java.lang.Exception' .class ∨ class = `java.lang.Throwable' .class
Proof step 17:
⊦ predef_supers(`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)

Rule argument

[x0lemmaarg: spec-name: predefined instance-name: lemma-name: predefined antecedent: succedent: is_predefined_class(class) ↔ class = `java.lang.Object' .class ∨ class = `*Array*' .class ∨ class = `java.lang.NullPointerException' .class ∨ class = `java.lang.ArithmeticException' .class ∨ class = `java.lang.ClassCastException' .class ∨ class = `java.lang.ArrayStoreException' .class ∨ class = `java.lang.NegativeArraySizeException' .class ∨ class = `java.lang.ArrayIndexOutOfBoundsException' .class ∨ class = `java.lang.IndexOutOfBoundsException' .class ∨ class = `java.lang.NoClassDefFoundError' .class ∨ class = `java.lang.ExceptionInInitializerError' .class ∨ class = `java.lang.Error' .class ∨ class = `java.lang.RuntimeException' .class ∨ class = `java.lang.Exception' .class ∨ class = `java.lang.Throwable' .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, a, ⊦ (classes + classes0) + classes1 = classes + classes0 + classes1], [CSIMPNAMEDSEQ : list, classnames, Two, ⊦ class + class0 = class ' + class0 '], [CSIMPNAMEDSEQ : list, classnames, c, ⊦ class + classes = class ' + classes], [CSIMPNAMEDSEQ : list, classnames, app-01, ⊦ classes + classes0 = classes + classes1 ↔ classes0 = classes1])], [EXTRATERMS : (class)]]