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Proof step 44 from proof same-subclasses-forward (previous step)

ty .jtelemtype = mkclasstype(`java.lang.Object' .class), is_arraytype(ty3), contains(str0, ty, ty3), has_classtype(ty), ty1 ≤ ty, type∃(str0, ty3), type∃(str0, ty1), type∃(str0, ty), is_reftype(ty), has_classtype(ty3), same-subclasses(`java.lang.Object' .class, str, str0), ∀ 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) ∧ ty3 ≤ ty2, is_arraytype(ty1) → ty3 ≤ ty1 .type ⊦ contains(str0, mkclasstype(`java.lang.Object' .class), ty3 .type .jtelemtype), same-subclasses(ty3 .type .jtelemtype .class, str, str0) ∧ (contains(str0, ty3 .type .jtelemtype, mkclasstype(class0)) → same-subclasses(class0, str, str0))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 43:
ty3 = mkarraytype(ty0), ty .jtelemtype = mkclasstype(`java.lang.Object' .class), is_arraytype(ty3), contains(str0, ty, ty3), has_classtype(ty), ty1 ≤ ty, type∃(str0, ty3), type∃(str0, ty1), type∃(str0, ty), is_reftype(ty), has_classtype(ty3), same-subclasses(`java.lang.Object' .class, str, str0), ∀ 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) ∧ ty3 ≤ ty2, is_arraytype(ty1) → ty3 ≤ 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))

Rule argument

[speclemmaarg: ,is_arraytype(ty) → (ty0 = ty .type ↔ ty = mkarraytype(ty0)) ,[ty, ty0] → [ty3, ty0] ,T ,javatype , ,elim-01 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ is_arraytype(ty) → ( ty0 = ty .type ↔ ty = mkarraytype(ty0))])], [EXTRATERMS : (ty3, ty0)]]