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Proof step 83 from proof same-subclasses-01 (previous step)

is_classtype(ty0), contains(str0, (ty0 ' + tys1) + mkclasstype(class0) '), mkfs(class1, ty1, fieldvar) ' ∈ instfields(class2), ty0 ≤ ty1, same-subclasses-contains(class, str, str0), tdname+∃(str0, class), class2 ≤ class, tdname+∃(str0, class2), ∀ class0, str0, str, class, tys0. # tys0 < # (ty0 + tys1) → (same-subclasses-contains(class, str, str0) ∧ contains(str0, mkclasstype(class) ' + tys0 + mkclasstype(class0) ') → tdname+∃(str, class0)) ⊦ class = `java.lang.Object' .class, tdname+∃(str, class0), interface∃(str0, class2)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 50:
⊦ is_classtype(ty) ↔ (∃ class. ty = mkclasstype(class))
Proof step 82:
∃ class. ty0 = mkclasstype(class), contains(str0, (ty0 ' + tys1) + mkclasstype(class0) '), mkfs(class1, ty1, fieldvar) ' ∈ instfields(class2), ty0 ≤ ty1, same-subclasses-contains(class, str, str0), tdname+∃(str0, class), class2 ≤ class, tdname+∃(str0, class2), ∀ class0, str0, str, class, tys0. # tys0 < # (ty0 + tys1) → (same-subclasses-contains(class, str, str0) ∧ contains(str0, mkclasstype(class) ' + tys0 + mkclasstype(class0) ') → tdname+∃(str, class0)) ⊦ class = `java.lang.Object' .class, tdname+∃(str, class0), interface∃(str0, class2)

Rule argument

[speclemmaarg: ,is_classtype(ty) ↔ (∃ class. ty = mkclasstype(class)) ,[ty] → [ty0] ,F ,javatype , ,ex-03 ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (ty0)]]