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Proof step 136 from proof same-subclasses-01 (previous step)

ty0 .jtelemtype = mkclasstype(class3), contains(str0, (ty0 ' + tys1) + mkclasstype(class0) '), mkfs(class1, ty1, fieldvar) ' ∈ instfields(class2), ty0 ≤ ty1, same-subclasses(class, str, str0), tdname+∃(str0, class), class2 ≤ class, tdname+∃(str0, class2), # tys ≤ # tys1, contains(str0, mkclasstype(class3) ' + tys + mkclasstype(class0) '), ∀ class0, str0, str, class, tys0. # tys0 < # (ty0 + tys1) → (same-subclasses-contains(class, str, str0) ∧ contains(str0, mkclasstype(class) ' + tys0 + mkclasstype(class0) ') → tdname+∃(str, class0)) ⊦ class = `java.lang.Object' .class, same-subclasses(class3, str, str0), is_classtype(ty0), tdname+∃(str, class0), interface∃(str0, class2), contains(str0, mkclasstype(class), mkclasstype(class3))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 127:
⊦ contains(str, ty, ty0) ↔ type∃(str, ty) ∧ is_reftype(ty) ∧ ( (∃ ty1. ty1 ≤ ty ∧ type∃(str, ty1) ∧ type∃(str, ty0) ∧ (is_classtype(ty1) → ¬ interface∃(str, ty1 .class) ∧ (∃ fs. fs ' ∈ instfields(ty1 .class) ∧ ty0 ≤ fs .type)) ∧ (is_arraytype(ty1) → ty0 ≤ ty1 .type)) ∨ (∃ ty1, ty2. ty1 ≤ ty ∧ type∃(str, ty1) ∧ (is_classtype(ty1) → ¬ interface∃(str, ty1 .class) ∧ (∃ fs. fs ' ∈ instfields(ty1 .class) ∧ ty2 ≤ fs .type)) ∧ (is_arraytype(ty1) → ty2 ≤ ty1 .type) ∧ contains(str, ty2, ty0)))
Proof step 135:
ty0 .jtelemtype = mkclasstype(class3), contains(str0, (ty0 ' + tys1) + mkclasstype(class0) '), mkfs(class1, ty1, fieldvar) ' ∈ instfields(class2), ty0 ≤ ty1, same-subclasses(class, str, str0), tdname+∃(str0, class), class2 ≤ class, tdname+∃(str0, class2), # tys ≤ # tys1, contains(str0, mkclasstype(class3) ' + tys + mkclasstype(class0) '), ∀ class0, str0, str, class, tys0. # tys0 < # (ty0 + tys1) → (same-subclasses-contains(class, str, str0) ∧ contains(str0, mkclasstype(class) ' + tys0 + mkclasstype(class0) ') → tdname+∃(str, class0)) ⊦ class = `java.lang.Object' .class, same-subclasses(class3, str, str0), is_classtype(ty0), tdname+∃(str, class0), interface∃(str0, class2), type∃(str0, mkclasstype(class)) ∧ is_reftype(mkclasstype(class)) ∧ ( (∃ ty1. ty1 ≤ mkclasstype(class) ∧ type∃(str0, ty1) ∧ type∃(str0, mkclasstype(class3)) ∧ (is_classtype(ty1) → ¬ interface∃(str0, ty1 .class) ∧ (∃ fs. fs ' ∈ instfields(ty1 .class) ∧ mkclasstype(class3) ≤ fs .type)) ∧ (is_arraytype(ty1) → mkclasstype(class3) ≤ ty1 .type)) ∨ (∃ ty1, ty2. ty1 ≤ mkclasstype(class) ∧ type∃(str0, ty1) ∧ (is_classtype(ty1) → ¬ interface∃(str0, ty1 .class) ∧ (∃ fs. fs ' ∈ instfields(ty1 .class) ∧ ty2 ≤ fs .type)) ∧ (is_arraytype(ty1) → ty2 ≤ ty1 .type) ∧ contains(str0, ty2, mkclasstype(class3))))

Rule argument

[crewrite-arg: contains-type-rec , F , [ty0, ty, str] → [mkclasstype(class3), mkclasstype(class), str0] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (mkclasstype(class3), mkclasstype(class), str0)]]