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Proof step 76 from proof contains-subspec-better (previous step)

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)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 56:
⊦ type∃(str, ty) ↔ ¬ has_classtype(ty) ∨ tdname+∃(str, ty .jtclass)
Proof step 75:
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), ¬ has_classtype(ty2) ∨ tdname+∃(str, ty2 .jtclass), ∃ 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

[speclemmaarg: ,type∃(str, ty) ↔ ¬ has_classtype(ty) ∨ tdname+∃(str, ty .jtclass) ,[ty, str] → [ty2, str] ,F ,typefuns , ,typeex-def ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (ty2, str)]]