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Proof step 152 from proof same-subclasses-01 (previous step)

tys + mkclasstype(class0) ' = ty3 ' + tys2, contains(str0, ty3 ' + tys2), type∃(str0, ty), ty ≤ ty0 .jtelemtype, is_reftype(ty0 .jtelemtype), type∃(str0, ty0 .jtelemtype), # tys ≤ # tys1, tdname+∃(str0, class2), class2 ≤ class, tdname+∃(str0, class), same-subclasses-contains(class, str, str0), ty0 ≤ ty1, mkfs(class1, ty1, fieldvar) ' ∈ instfields(class2), contains(str0, (ty0 ' + tys1) + mkclasstype(class0) '), is_classtype(ty) → ¬ interface∃(str0, ty .class) ∧ mkfs(class3, ty2, fieldvar0) ' ∈ instfields(ty .class) ∧ ty3 ≤ ty2, is_arraytype(ty) → ty3 ≤ ty .type, ∀ class0, str0, str, class, tys0. # tys0 < # (ty0 + tys1) → (same-subclasses-contains(class, str, str0) ∧ contains(str0, mkclasstype(class) ' + tys0 + mkclasstype(class0) ') → tdname+∃(str, class0)) ⊦ class = `java.lang.Object' .class, interface∃(str0, class2), tdname+∃(str, class0), has_classtype(ty0), same-subclasses-contains(ty0 .jtelemtype .class, str, str0) ∧ contains(str0, mkclasstype(ty0 .jtelemtype .class) ' + ty3 ' + tys2), mkclasstype(class0) ≠ ty3 ∧ ¬ mkclasstype(class0) ∈ tys2, ¬ ty3 ∈ tys ∧ ty3 ≠ mkclasstype(class0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 149:
⊦ is_reftype(ty) ↔ is_classtype(ty) ∨ is_arraytype(ty)
Proof step 151:
tys + mkclasstype(class0) ' = ty3 ' + tys2, contains(str0, ty3 ' + tys2), type∃(str0, ty), ty ≤ ty0 .jtelemtype, is_classtype(ty0 .jtelemtype) ∨ is_arraytype(ty0 .jtelemtype), type∃(str0, ty0 .jtelemtype), # tys ≤ # tys1, tdname+∃(str0, class2), class2 ≤ class, tdname+∃(str0, class), same-subclasses-contains(class, str, str0), ty0 ≤ ty1, mkfs(class1, ty1, fieldvar) ' ∈ instfields(class2), contains(str0, (ty0 ' + tys1) + mkclasstype(class0) '), is_classtype(ty) → ¬ interface∃(str0, ty .class) ∧ mkfs(class3, ty2, fieldvar0) ' ∈ instfields(ty .class) ∧ ty3 ≤ ty2, is_arraytype(ty) → ty3 ≤ ty .type, ∀ class0, str0, str, class, tys0. # tys0 < # (ty0 + tys1) → (same-subclasses-contains(class, str, str0) ∧ contains(str0, mkclasstype(class) ' + tys0 + mkclasstype(class0) ') → tdname+∃(str, class0)) ⊦ class = `java.lang.Object' .class, interface∃(str0, class2), tdname+∃(str, class0), has_classtype(ty0), same-subclasses-contains(ty0 .jtelemtype .class, str, str0) ∧ contains(str0, mkclasstype(ty0 .jtelemtype .class) ' + ty3 ' + tys2), mkclasstype(class0) ≠ ty3 ∧ ¬ mkclasstype(class0) ∈ tys2, ¬ ty3 ∈ tys ∧ ty3 ≠ mkclasstype(class0)

Rule argument

[speclemmaarg: ,is_reftype(ty) ↔ is_classtype(ty) ∨ is_arraytype(ty) ,[ty] → [ty0 .jtelemtype] ,F ,typefuns , ,is-reftype ]

Additional information

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