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Proof step 77 from proof contains-subspec-better (previous step)

ty = mkclasstype(`java.lang.Object' .class), ty3 ≤ ty2, contains(str0, (ty3 ' + tys1) + ty0 '), type∃(str0, ty2), is_reftype(ty), type∃(str, ty), same-subclasses(ty .jtelemtype .class, str, str0), has_classtype(ty), type∃(str0, ty0), contains(str0, ty, ty0), type∃(str, ty3), type∃(str0, ty3), type∃(str, ty0), type∃(str0, ty), contains(str, ty3, ty0), has_classtype(ty2), ∀ class0. contains(str0, ty .jtelemtype, mkclasstype(class0)) → same-subclasses(class0, 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) ⊦ ty = ty3, ty ∈ tys1, ty3 ∈ tys1, dups(tys1), type∃(str, ty2), ∃ ty4. ty4 ≤ ty ∧ type∃(str, ty4) ∧ (is_classtype(ty4) → ¬ interface∃(str, ty4 .class) ∧ (∃ fs. fs ' ∈ instfields(ty4 .class) ∧ ty0 ≤ fs .type)) ∧ (is_arraytype(ty4) → ty0 ≤ ty4 .type)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 76:
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 '), type∃(str0, ty2), same-subclasses(`java.lang.Object' .class, str, str0), ∀ 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, mkclasstype(`java.lang.Object' .class) ∈ tys1, ty3 ∈ tys1, dups(tys1), type∃(str, ty2), ∃ 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

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ type∃(str, ty) → ( ty ≤ mkclasstype (`java.lang.Object' .class) ↔ is_classtype(ty) ∨ is_arraytype(ty))], [CSIMPSEQ : ⊦ has_classtype(mkclasstype(class))], [CSIMPSEQ : ⊦ mkclasstype(class) .class = class], [CSIMPSEQ : ⊦ mkclasstype(class) .jtelemtype = mkclasstype(class)], [CSIMPSEQ : ⊦ tdname+∃ (str, `java.lang.Object' .class)], [CSIMPSEQ : ⊦ type∃(str, mkclasstype(class)) ↔ tdname+∃(str, class)], [CSIMPSEQ : ⊦ is_reftype(mkclasstype(class))])]]