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Proof step 164 from proof contains-subspec-better (previous step)

ty .jtelemtype = mkclasstype(`java.lang.Object' .class), tys + ty0 ' = ty3 ' + tys1, type∃(str, ty), is_reftype(ty), ty1 ≤ ty, type∃(str0, ty1), contains(str0, ty3 ' + tys1), type∃(str0, ty), type∃(str, ty0), type∃(str0, ty3), ty3 ∈ tys, ty0 ∈ tys1, contains(str0, ty, ty3), has_classtype(ty3), contains(str0, ty, ty0), type∃(str0, ty0), has_classtype(ty), same-subclasses(`java.lang.Object' .class, str, str0), is_arraytype(ty1) → ty3 ≤ ty1 .type, is_classtype(ty1) → ¬ interface∃(str0, ty1 .class) ∧ mkfs(class, ty2, fieldvar) ' ∈ instfields(ty1 .class) ∧ ty3 ≤ ty2, ∀ ty0, str0, str, ty, tys0. # tys0 < # tys → ( has_classtype(ty) ∧ same-subclasses-contains(ty .jtelemtype .class, str, str0) ∧ type∃(str, ty) ∧ contains(str0, ty ' + tys0 + ty0 ') → contains(str, ty, ty0) ∨ dups(tys0) ∨ ty ∈ tys0) ⊦ contains(str0, mkclasstype(`java.lang.Object' .class), ty3 .jtelemtype), type∃(str, ty3), contains(str, ty, ty0), dups(tys), ty ∈ tys, ty3 .jtelemtype ≤ mkclasstype(`java.lang.Object' .class)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 161:
⊦ has_classtype(ty) ↔ is_classtype(ty .jtelemtype)
Proof step 163:
ty .jtelemtype = mkclasstype(`java.lang.Object' .class), tys + ty0 ' = ty3 ' + tys1, type∃(str, ty), is_reftype(ty), ty1 ≤ ty, type∃(str0, ty1), contains(str0, ty3 ' + tys1), type∃(str0, ty), type∃(str, ty0), type∃(str0, ty3), ty3 ∈ tys, ty0 ∈ tys1, contains(str0, ty, ty3), is_classtype(ty3 .jtelemtype), contains(str0, ty, ty0), type∃(str0, ty0), has_classtype(ty), same-subclasses(`java.lang.Object' .class, str, str0), is_arraytype(ty1) → ty3 ≤ ty1 .type, is_classtype(ty1) → ¬ interface∃(str0, ty1 .class) ∧ mkfs(class, ty2, fieldvar) ' ∈ instfields(ty1 .class) ∧ ty3 ≤ ty2, ∀ ty0, str0, str, ty, tys0. # tys0 < # tys → ( has_classtype(ty) ∧ same-subclasses-contains(ty .jtelemtype .class, str, str0) ∧ type∃(str, ty) ∧ contains(str0, ty ' + tys0 + ty0 ') → contains(str, ty, ty0) ∨ dups(tys0) ∨ ty ∈ tys0) ⊦ contains(str0, mkclasstype(`java.lang.Object' .class), ty3 .jtelemtype), type∃(str, ty3), contains(str, ty, ty0), dups(tys), ty ∈ tys, ty3 .jtelemtype ≤ mkclasstype(`java.lang.Object' .class)

Rule argument

[speclemmaarg: ,has_classtype(ty) ↔ is_classtype(ty .jtelemtype) ,[ty] → [ty3] ,F ,typefuns , ,has-classtype ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (ty3)]]