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Proof step 36 from proof same-subclasses-forward (previous step)

ty .jtelemtype = mkclasstype(`java.lang.Object' .class), ty0 .jtelemtype .class ≤ `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), contains(str0, ty0 .jtelemtype, mkclasstype(class0)), 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(class0, str, str0), contains(str0, mkclasstype(`java.lang.Object' .class), mkclasstype(class0)), ty0 .jtelemtype ≤ mkclasstype(`java.lang.Object' .class)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 34:
⊦ has_classtype(ty) ↔ is_classtype(ty .jtelemtype)
Proof step 35:
ty .jtelemtype = mkclasstype(`java.lang.Object' .class), ty0 .jtelemtype .class ≤ `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), is_classtype(ty0 .jtelemtype), contains(str0, ty0 .jtelemtype, mkclasstype(class0)), 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(class0, str, str0), contains(str0, mkclasstype(`java.lang.Object' .class), mkclasstype(class0)), ty0 .jtelemtype ≤ mkclasstype(`java.lang.Object' .class)

Rule argument

[speclemmaarg: ,has_classtype(ty) ↔ is_classtype(ty .jtelemtype) ,[ty] → [ty0] ,F ,typefuns , ,has-classtype ]

Additional information

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