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Proof step 24 from proof superClass-predef (previous step)

is_predefined_class(class) ⊦ is_predefined_class(predef_superClass(class))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ 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 3:
⊦ predef_superClass(`java.lang.Object' .class) = `java.lang.Object' .class
Proof step 4:
⊦ is_predefined_class(`java.lang.Object' .class)
Proof step 5:
⊦ predef_superClass(`*Array*' .class) = `java.lang.Object' .class
Proof step 6:
⊦ predef_superClass(`java.lang.NullPointerException' .class) = `java.lang.RuntimeException' .class
Proof step 7:
⊦ is_predefined_class(`java.lang.RuntimeException' .class)
Proof step 8:
⊦ predef_superClass(`java.lang.ArithmeticException' .class) = `java.lang.RuntimeException' .class
Proof step 9:
⊦ predef_superClass(`java.lang.ClassCastException' .class) = `java.lang.RuntimeException' .class
Proof step 10:
⊦ predef_superClass(`java.lang.ArrayStoreException' .class) = `java.lang.RuntimeException' .class
Proof step 11:
⊦ predef_superClass(`java.lang.NegativeArraySizeException' .class) = `java.lang.RuntimeException' .class
Proof step 12:
⊦ predef_superClass(`java.lang.ArrayIndexOutOfBoundsException' .class) = `java.lang.IndexOutOfBoundsException' .class
Proof step 13:
⊦ is_predefined_class(`java.lang.IndexOutOfBoundsException' .class)
Proof step 14:
⊦ predef_superClass(`java.lang.IndexOutOfBoundsException' .class) = `java.lang.RuntimeException' .class
Proof step 15:
⊦ predef_superClass(`java.lang.NoClassDefFoundError' .class) = `java.lang.Error' .class
Proof step 16:
⊦ is_predefined_class(`java.lang.Error' .class)
Proof step 17:
⊦ predef_superClass(`java.lang.ExceptionInInitializerError' .class) = `java.lang.Error' .class
Proof step 18:
⊦ predef_superClass(`java.lang.Error' .class) = `java.lang.Throwable' .class
Proof step 19:
⊦ is_predefined_class(`java.lang.Throwable' .class)
Proof step 20:
⊦ predef_superClass(`java.lang.RuntimeException' .class) = `java.lang.Exception' .class
Proof step 21:
⊦ is_predefined_class(`java.lang.Exception' .class)
Proof step 22:
⊦ predef_superClass(`java.lang.Exception' .class) = `java.lang.Throwable' .class
Proof step 23:
⊦ predef_superClass(`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 : ()], [EXTRATERMS : (class)]]