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Proof step 42 from proof same-subclasses-forward (previous step)

ty .jtelemtype = mkclasstype(`java.lang.Object' .class), same-subclasses(`java.lang.Object' .class, str, str0), contains(str0, ty, mkarraytype(ty0)), has_classtype(ty), ty1 ≤ ty, type∃(str0, ty0), type∃(str0, ty1), type∃(str0, ty), is_reftype(ty), has_classtype(ty0), ∀ class0. contains(str0, mkclasstype(`java.lang.Object' .class), mkclasstype(class0)) → same-subclasses(class0, str, str0), is_classtype(ty1) → ¬ interface∃(str0, ty1 .class) ∧ mkfs(class, ty2, fieldvar) ' ∈ instfields(ty1 .class) ∧ mkarraytype(ty0) ≤ ty2, is_arraytype(ty1) → mkarraytype(ty0) ≤ ty1 .type ⊦ contains(str0, mkclasstype(`java.lang.Object' .class), ty0 .jtelemtype), same-subclasses(ty0 .jtelemtype .class, str, str0) ∧ (contains(str0, ty0 .jtelemtype, mkclasstype(class0)) → same-subclasses(class0, str, str0))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 26:
⊦ same-subclasses(class, str, str0) ∧ class0 ≤ class → same-subclasses(class0, str, str0)
Proof step 32:
¬ (same-subclasses(`java.lang.Object' .class, str, str0) ∧ ty0 .jtelemtype .class ≤ `java.lang.Object' .class), ty .jtelemtype = mkclasstype(`java.lang.Object' .class), same-subclasses(`java.lang.Object' .class, str, str0), contains(str0, ty, mkarraytype(ty0)), has_classtype(ty), ty1 ≤ ty, type∃(str0, ty0), type∃(str0, ty1), type∃(str0, ty), is_reftype(ty), has_classtype(ty0), ∀ class0. contains(str0, mkclasstype(`java.lang.Object' .class), mkclasstype(class0)) → same-subclasses(class0, str, str0), is_classtype(ty1) → ¬ interface∃(str0, ty1 .class) ∧ mkfs(class, ty2, fieldvar) ' ∈ instfields(ty1 .class) ∧ mkarraytype(ty0) ≤ ty2, is_arraytype(ty1) → mkarraytype(ty0) ≤ ty1 .type ⊦ contains(str0, mkclasstype(`java.lang.Object' .class), ty0 .jtelemtype), same-subclasses(ty0 .jtelemtype .class, str, str0) ∧ (contains(str0, ty0 .jtelemtype, mkclasstype(class0)) → same-subclasses(class0, str, str0))
Proof step 41:
same-subclasses(`java.lang.Object' .class, str, str0) ∧ ty0 .jtelemtype .class ≤ `java.lang.Object' .class, ty .jtelemtype = mkclasstype(`java.lang.Object' .class), same-subclasses(`java.lang.Object' .class, str, str0), contains(str0, ty, mkarraytype(ty0)), has_classtype(ty), ty1 ≤ ty, type∃(str0, ty0), type∃(str0, ty1), type∃(str0, ty), is_reftype(ty), has_classtype(ty0), ∀ class0. contains(str0, mkclasstype(`java.lang.Object' .class), mkclasstype(class0)) → same-subclasses(class0, str, str0), is_classtype(ty1) → ¬ interface∃(str0, ty1 .class) ∧ mkfs(class, ty2, fieldvar) ' ∈ instfields(ty1 .class) ∧ mkarraytype(ty0) ≤ ty2, is_arraytype(ty1) → mkarraytype(ty0) ≤ ty1 .type ⊦ contains(str0, mkclasstype(`java.lang.Object' .class), ty0 .jtelemtype), true ∧ (contains(str0, ty0 .jtelemtype, mkclasstype(class0)) → same-subclasses(class0, str, str0))

Rule argument

[speclemmaarg: , same-subclasses(class, str, str0) ∧ class0 ≤ class → same-subclasses(class0, str, str0) ,[class, str, str0, class0] → [`java.lang.Object' .class, str, str0, ty0 .jtelemtype .class] ,F ,junkrefs , ,same-subclasses-subclass ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (`java.lang.Object' .class, str, str0, ty0 .jtelemtype .class)]]