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Proof step 69 from proof contains-subspec-better (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 68:
class+∃(str0, ty2 .jtelemtype .class), contains(str0, (ty3 ' + tys1) + ty0 '), ty3 ≤ ty2, has_classtype(ty2), contains(str, ty3, ty0), type∃(str, ty0), type∃(str0, ty3), type∃(str, ty3), contains(str0, mkclasstype(`java.lang.Object' .class), ty0), type∃(str0, ty0), ∀ class. interface∃(str0, class) → interface∃(str, class), ∀ class. class∃(str0, class) → class∃(str, class), ∀ class. contains(str0, mkclasstype(`java.lang.Object' .class), mkclasstype(class)) → same-subclasses(class, str, str0), ∀ ty0, str0, str, ty, tys0. # tys0 < # (ty3 + tys1) → ( 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) ⊦ mkclasstype(`java.lang.Object' .class) = ty3, interface∃(str0, ty2 .jtelemtype .class), tdname+∃(str, ty2 .jtelemtype .class), dups(tys1), ty3 ∈ tys1, mkclasstype(`java.lang.Object' .class) ∈ tys1, ∃ ty. (is_classtype(ty) ∨ is_arraytype(ty)) ∧ type∃(str, ty) ∧ (is_classtype(ty) → ¬ interface∃(str, ty .class) ∧ (∃ fs. fs ' ∈ instfields(ty .class) ∧ ty0 ≤ fs .type)) ∧ (is_arraytype(ty) → ty0 ≤ ty .type)

Rule argument

[emptyarg]

Additional information

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