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Proof step 88 from proof contains-subspec-better (previous step)

ty3 ≤ ty2, contains(str0, (ty3 ' + tys1) + ty0 '), type∃(str0, ty2), mkarraytype(ty2) ≤ ty, 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)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 55:
⊦ mkarraytype(ty) ≤ ty0 ↔ ty0 = mkclasstype(`java.lang.Object' .class) ∨ is_arraytype(ty0) ∧ ty ≤ ty0 .type
Proof step 87:
ty3 ≤ ty2, contains(str0, (ty3 ' + tys1) + ty0 '), type∃(str0, ty2), ty = mkclasstype(`java.lang.Object' .class) ∨ is_arraytype(ty) ∧ ty2 ≤ ty .type, 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)

Rule argument

[speclemmaarg: , mkarraytype(ty) ≤ ty0 ↔ ty0 = mkclasstype(`java.lang.Object' .class) ∨ is_arraytype(ty0) ∧ ty ≤ ty0 .type ,[ty0, ty] → [ty, ty2] ,F ,typefuns , ,array-le ]

Additional information

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