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Proof step 34 from proof same-subclasses-01 (previous step)

same-subclasses-contains(class, str, str0), tdname+∃(str0, class), is_classtype(ty), ty .class ≤ class, type∃(str0, ty), tdname+∃(str0, class0), mkfs(class1, ty0, fieldvar) ' ∈ instfields(ty .class), is_classtype(ty0), class0 ≤ ty0 .class, ∀ class0, str0, str, class, tys0. # tys0 < # [] → (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, ty .class)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 33:
ty = mkclasstype(class2), same-subclasses-contains(class, str, str0), tdname+∃(str0, class), is_classtype(ty), class2 ≤ class, type∃(str0, ty), tdname+∃(str0, class0), mkfs(class1, ty0, fieldvar) ' ∈ instfields(class2), is_classtype(ty0), class0 ≤ ty0 .class, ∀ class0, str0, str, class, tys0. # tys0 < # [] → (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 .class ↔ ty = mkclasstype(class)) ,[ty, class] → [ty, class2] ,T ,javatype , ,elim-02 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ is_classtype(ty) → ( class = ty .class ↔ ty = mkclasstype(class))])], [EXTRATERMS : (ty, class2)]]