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Proof step 139 from proof contains-subspec-better (previous step)

contains(str0, ty .jtelemtype, mkclasstype(ty3 .jtelemtype .class)), tys + ty0 ' = ty3 ' + tys1, contains(str0, ty, ty0), type∃(str0, ty0), has_classtype(ty), same-subclasses(ty .jtelemtype .class, str, str0), type∃(str, ty), is_reftype(ty), ty1 ≤ ty, type∃(str0, ty1), contains(str0, ty3 ' + tys1), type∃(str0, ty), type∃(str, ty0), type∃(str0, ty3), ty3 ∈ tys, ty0 ∈ tys1, is_arraytype(ty1) → ty3 ≤ ty1 .type, is_classtype(ty1) → ¬ interface∃(str0, ty1 .class) ∧ mkfs(class, ty2, fieldvar) ' ∈ instfields(ty1 .class) ∧ ty3 ≤ ty2, contains(str0, ty .jtelemtype, mkclasstype(ty3 .jtelemtype .class)) → same-subclasses(ty3 .jtelemtype .class, str, str0), ∀ ty0, str0, str, ty, tys0. # tys0 < # tys → ( 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) ⊦ type∃(str, ty3), contains(str, ty, ty0), dups(tys), ty ∈ tys

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 138:
tys + ty0 ' = ty3 ' + tys1, contains(str0, ty .jtelemtype, mkclasstype(ty3 .jtelemtype .class)), contains(str0, ty, ty0), type∃(str0, ty0), has_classtype(ty), same-subclasses(ty .jtelemtype .class, str, str0), type∃(str, ty), is_reftype(ty), ty1 ≤ ty, type∃(str0, ty1), contains(str0, ty3 ' + tys1), type∃(str0, ty), type∃(str, ty0), type∃(str0, ty3), ty3 ∈ tys, ty0 ∈ tys1, same-subclasses(ty3 .jtelemtype .class, str, str0), is_arraytype(ty1) → ty3 ≤ ty1 .type, is_classtype(ty1) → ¬ interface∃(str0, ty1 .class) ∧ mkfs(class, ty2, fieldvar) ' ∈ instfields(ty1 .class) ∧ ty3 ≤ ty2, ∀ ty0, str0, str, ty, tys0. # tys0 < # tys → ( 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) ⊦ type∃(str, ty3), contains(str, ty, ty0), dups(tys), ty ∈ tys

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ()]]