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Proof step 58 from proof same-subclasses-forward (previous step)

contains(str0, ty, ty3), same-subclasses(ty .jtelemtype .class, str, str0), has_classtype(ty3), is_reftype(ty), type∃(str0, ty), type∃(str0, ty1), type∃(str0, ty3), ty1 ≤ ty, is_arraytype(ty1) → ty3 ≤ ty1 .type, is_classtype(ty1) → ¬ interface∃(str0, ty1 .class) ∧ mkfs(class, ty2, fieldvar) ' ∈ instfields(ty1 .class) ∧ ty3 ≤ ty2, ∀ class0. contains(str0, mkclasstype(ty .jtelemtype .class), mkclasstype(class0)) → same-subclasses(class0, str, str0), contains(str0, mkclasstype(ty .jtelemtype .class), ty3 .jtelemtype) → same-subclasses(ty3 .jtelemtype .class, str, str0) ⊦ same-subclasses(ty3 .jtelemtype .class, str, str0) ∧ (contains(str0, ty3 .jtelemtype, mkclasstype(class0)) → same-subclasses(class0, str, str0))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ has_classtype(ty) → mkclasstype(ty .jtelemtype .class) = ty .jtelemtype
Proof step 4:
⊦ ¬ has_classtype(ty) ∧ has_classtype(ty0) → ¬ contains(str, ty, ty0)
Proof step 57:
has_classtype(ty), contains(str0, ty, ty3), same-subclasses(ty .jtelemtype .class, str, str0), has_classtype(ty3), is_reftype(ty), type∃(str0, ty), type∃(str0, ty1), type∃(str0, ty3), ty1 ≤ ty, is_arraytype(ty1) → ty3 ≤ ty1 .type, is_classtype(ty1) → ¬ interface∃(str0, ty1 .class) ∧ mkfs(class, ty2, fieldvar) ' ∈ instfields(ty1 .class) ∧ ty3 ≤ ty2, ∀ class0. contains(str0, ty .jtelemtype, mkclasstype(class0)) → same-subclasses(class0, str, str0), contains(str0, ty .jtelemtype, ty3 .jtelemtype) → same-subclasses(ty3 .jtelemtype .class, str, str0) ⊦ same-subclasses(ty3 .jtelemtype .class, str, str0) ∧ (contains(str0, ty3 .jtelemtype, mkclasstype(class0)) → same-subclasses(class0, str, str0))

Rule argument

[speclemmaarg: , has_classtype(ty) → mkclasstype(ty .jtelemtype .class) = ty .jtelemtype ,[ty] → [ty] ,F ,typefuns , ,jtelemtype-01 ]

Additional information

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