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Proof step 48 from proof same-subclasses-forward (previous step)

ty3 = mkclasstype(class1), ty .jtelemtype = mkclasstype(`java.lang.Object' .class), same-subclasses(`java.lang.Object' .class, str, str0), contains(str0, ty, ty3), has_classtype(ty), ty1 ≤ ty, type∃(str0, ty3), type∃(str0, ty1), type∃(str0, ty), is_reftype(ty), is_classtype(ty3), ∀ class0. contains(str0, mkclasstype(`java.lang.Object' .class), mkclasstype(class0)) → same-subclasses(class0, str, str0), is_classtype(ty1) → ¬ interface∃(str0, ty1 .class) ∧ mkfs(class, ty2, fieldvar) ' ∈ instfields(ty1 .class) ∧ ty3 ≤ ty2, is_arraytype(ty1) → ty3 ≤ ty1 .type ⊦ contains(str0, mkclasstype(`java.lang.Object' .class), ty3), same-subclasses(class1, str, str0) ∧ (contains(str0, ty3, mkclasstype(class0)) → same-subclasses(class0, str, str0))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 47:
ty .jtelemtype = mkclasstype(`java.lang.Object' .class), type∃(str0, ty1), type∃(str0, ty), is_reftype(ty), same-subclasses(`java.lang.Object' .class, str, str0), contains(str0, ty, mkclasstype(class1)), has_classtype(ty), ty1 ≤ ty, tdname+∃(str0, class1), ∀ class0. contains(str0, mkclasstype(`java.lang.Object' .class), mkclasstype(class0)) → same-subclasses(class0, str, str0), is_classtype(ty1) → ¬ interface∃(str0, ty1 .class) ∧ mkfs(class, ty2, fieldvar) ' ∈ instfields(ty1 .class) ∧ is_classtype(ty2) ∧ class1 ≤ ty2 .class, is_arraytype(ty1) → is_classtype(ty1 .type) ∧ class1 ≤ ty1 .type .class ⊦ contains(str0, mkclasstype(`java.lang.Object' .class), mkclasstype(class1)), same-subclasses(class1, str, str0) ∧ (contains(str0, mkclasstype(class1), mkclasstype(class0)) → same-subclasses(class0, str, str0))

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ mkclasstype(class) ≤ ty ↔ is_classtype(ty) ∧ class ≤ ty .class], [CSIMPSEQ : ⊦ is_classtype(mkclasstype(class))], [CSIMPSEQ : ⊦ type∃(str, mkclasstype(class)) ↔ tdname+∃(str, class)])]]