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Proof step 131 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)) ⊦ contains(str0, ty0, mkclasstype(class3)), class = `java.lang.Object' .class, same-subclasses(class3, str, str0), is_classtype(ty0), tdname+∃(str, class0), interface∃(str0, class2), ∃ ty. ty ≤ mkclasstype(class) ∧ type∃(str0, ty) ∧ tdname+∃(str0, class3) ∧ (is_classtype(ty) → ¬ interface∃(str0, ty .class) ∧ (∃ fs. fs ' ∈ instfields(ty .class) ∧ mkclasstype(class3) ≤ fs .type)) ∧ (is_arraytype(ty) → mkclasstype(class3) ≤ ty .type)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 129:
⊦ ty .jtelemtype = ty0 ∧ ty ≠ ty0 ∧ type∃(str, ty) → contains(str, ty, ty0)
Proof step 130:
⊦ ¬ type∃(str, ty) → ¬ contains(str, ty ' + tys)

Rule argument

[crewrite-arg: contains-array-elemtype-04 , F , [ty0, ty, str] → [mkclasstype(class3), ty0, str0] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ mkclasstype(class) .jtelemtype = mkclasstype(class)], [CSIMPSEQ : ⊦ mkclasstype(class) = mkclasstype(class0) ↔ class = class0], [CSIMPSEQ : ⊦ mkclasstype(class) ≤ ty ↔ is_classtype(ty) ∧ class ≤ ty .class], [CSIMPSEQ : ⊦ is_classtype(mkclasstype(class))], [CSIMPSEQ : ⊦ (tys + tys0) + tys1 = tys + tys0 + tys1])], [EXTRATERMS : (mkclasstype(class3), ty0, str0)]]