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Proof step 29 from proof same-subclasses-forward (previous step)

ty .jtelemtype = mkclasstype(`java.lang.Object' .class), has_classtype(ty0), is_reftype(ty), type∃(str0, ty), type∃(str0, ty1), type∃(str0, ty0), ty1 ≤ ty, has_classtype(ty), contains(str0, ty, mkarraytype(ty0)), same-subclasses(`java.lang.Object' .class, str, str0), is_arraytype(ty1) → mkarraytype(ty0) ≤ ty1 .type, is_classtype(ty1) → ¬ interface∃(str0, ty1 .class) ∧ mkfs(class, ty2, fieldvar) ' ∈ instfields(ty1 .class) ∧ mkarraytype(ty0) ≤ ty2, ∀ class0. contains(str0, mkclasstype(`java.lang.Object' .class), mkclasstype(class0)) → same-subclasses(class0, str, str0) ⊦ tdname+∃(str0, ty0 .jtelemtype .class), ty0 .jtelemtype .class ≤ `java.lang.Object' .class, 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 28:
⊦ type∃(str, ty) ↔ ¬ has_classtype(ty) ∨ tdname+∃(str, ty .jtclass)

Rule argument

[speclemmaarg: ,type∃(str, ty) ↔ ¬ has_classtype(ty) ∨ tdname+∃(str, ty .jtclass) ,[ty, str] → [ty0, str0] ,F ,typefuns , ,typeex-def ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ty .jtclass = ty .jtelemtype .class])], [EXTRATERMS : (ty0, str0)]]