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Proof step 30 from proof superClass-supers (previous step)

is_predefined_class(class) ⊦ class = `java.lang.Object' .class, predef_superClass(class) = predef_supers(class) .rest .first

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
⊦ 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 2:
⊦ predef_superClass(`*Array*' .class) = `java.lang.Object' .class
Proof step 3:
⊦ predef_supers(`*Array*' .class) = `*Array*' .class + `java.lang.Object' .class
Proof step 4:
⊦ predef_superClass(`java.lang.NullPointerException' .class) = `java.lang.RuntimeException' .class
Proof step 5:
⊦ predef_supers(`java.lang.NullPointerException' .class) = `java.lang.NullPointerException' .class + `java.lang.RuntimeException' .class + `java.lang.Exception' .class + (`java.lang.Throwable' .class + `java.lang.Object' .class)
Proof step 6:
⊦ predef_superClass(`java.lang.ArithmeticException' .class) = `java.lang.RuntimeException' .class
Proof step 7:
⊦ predef_supers(`java.lang.ArithmeticException' .class) = `java.lang.ArithmeticException' .class + `java.lang.RuntimeException' .class + `java.lang.Exception' .class + (`java.lang.Throwable' .class + `java.lang.Object' .class)
Proof step 8:
⊦ predef_superClass(`java.lang.ClassCastException' .class) = `java.lang.RuntimeException' .class
Proof step 9:
⊦ predef_supers(`java.lang.ClassCastException' .class) = `java.lang.ClassCastException' .class + `java.lang.RuntimeException' .class + `java.lang.Exception' .class + (`java.lang.Throwable' .class + `java.lang.Object' .class)
Proof step 10:
⊦ predef_superClass(`java.lang.ArrayStoreException' .class) = `java.lang.RuntimeException' .class
Proof step 11:
⊦ predef_supers(`java.lang.ArrayStoreException' .class) = `java.lang.ArrayStoreException' .class + `java.lang.RuntimeException' .class + `java.lang.Exception' .class + (`java.lang.Throwable' .class + `java.lang.Object' .class)
Proof step 12:
⊦ predef_superClass(`java.lang.NegativeArraySizeException' .class) = `java.lang.RuntimeException' .class
Proof step 13:
⊦ predef_supers(`java.lang.NegativeArraySizeException' .class) = `java.lang.NegativeArraySizeException' .class + `java.lang.RuntimeException' .class + `java.lang.Exception' .class + (`java.lang.Throwable' .class + `java.lang.Object' .class)
Proof step 14:
⊦ predef_superClass(`java.lang.ArrayIndexOutOfBoundsException' .class) = `java.lang.IndexOutOfBoundsException' .class
Proof step 15:
⊦ 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)
Proof step 16:
⊦ predef_superClass(`java.lang.IndexOutOfBoundsException' .class) = `java.lang.RuntimeException' .class
Proof step 17:
⊦ predef_supers(`java.lang.IndexOutOfBoundsException' .class) = `java.lang.IndexOutOfBoundsException' .class + `java.lang.RuntimeException' .class + `java.lang.Exception' .class + (`java.lang.Throwable' .class + `java.lang.Object' .class)
Proof step 18:
⊦ predef_superClass(`java.lang.NoClassDefFoundError' .class) = `java.lang.Error' .class
Proof step 19:
⊦ predef_supers(`java.lang.NoClassDefFoundError' .class) = `java.lang.NoClassDefFoundError' .class + `java.lang.Error' .class + (`java.lang.Throwable' .class + `java.lang.Object' .class)
Proof step 20:
⊦ predef_superClass(`java.lang.ExceptionInInitializerError' .class) = `java.lang.Error' .class
Proof step 21:
⊦ predef_supers(`java.lang.ExceptionInInitializerError' .class) = `java.lang.ExceptionInInitializerError' .class + `java.lang.Error' .class + (`java.lang.Throwable' .class + `java.lang.Object' .class)
Proof step 22:
⊦ predef_superClass(`java.lang.Error' .class) = `java.lang.Throwable' .class
Proof step 23:
⊦ predef_supers(`java.lang.Error' .class) = `java.lang.Error' .class + (`java.lang.Throwable' .class + `java.lang.Object' .class)
Proof step 24:
⊦ predef_superClass(`java.lang.RuntimeException' .class) = `java.lang.Exception' .class
Proof step 25:
⊦ predef_supers(`java.lang.RuntimeException' .class) = `java.lang.RuntimeException' .class + `java.lang.Exception' .class + (`java.lang.Throwable' .class + `java.lang.Object' .class)
Proof step 26:
⊦ predef_superClass(`java.lang.Exception' .class) = `java.lang.Throwable' .class
Proof step 27:
⊦ predef_supers(`java.lang.Exception' .class) = `java.lang.Exception' .class + (`java.lang.Throwable' .class + `java.lang.Object' .class)
Proof step 28:
⊦ predef_superClass(`java.lang.Throwable' .class) = `java.lang.Object' .class
Proof step 29:
⊦ predef_supers(`java.lang.Throwable' .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, Two, ⊦ class + class0 = class ' + class0 '], [CSIMPNAMEDSEQ : list, classnames, c-07, ⊦ (class ' + classes) .rest = classes], [CSIMPNAMEDSEQ : list, classnames, a, ⊦ (classes + classes0) + classes1 = classes + classes0 + classes1], [CSIMPNAMEDSEQ : list, classnames, first, ⊦ class ' .first = class], [CSIMPNAMEDSEQ : classname, , inj, ⊦ stringvar .class = stringvar0 .class ↔ stringvar = stringvar0], [CSIMPNAMEDSEQ : list, classnames, c, ⊦ class + classes = class ' + classes], [CSIMPNAMEDSEQ : list, classnames, c-08, ⊦ (class ' + classes) .first = class])], [EXTRATERMS : (class)]]