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Proof step 163 from proof same-subclasses-01 (previous step)

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

User applied rule insert lemma

And obtained the following new goals

Proof step 84:
contains(str, ty + (tys + mkclasstype(class))), ¬ mkclasstype(class) ≤ ty .jtelemtype ⊦ ∃ tys1. # tys1 ≤ # tys ∧ contains(str, ty .jtelemtype + (tys1 + mkclasstype(class)))
Proof step 107:
contains(str0, (ty0 ' + tys1) + mkclasstype(class0) '), mkfs(class1, ty1, fieldvar) ' ∈ instfields(class2), ty0 ≤ ty1, same-subclasses-contains(class, str, str0), tdname+∃(str0, class), class2 ≤ class, tdname+∃(str0, class2), ∀ 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 + (tys1 + mkclasstype(class0))) ∧ ¬ mkclasstype(class0) ≤ ty0 .jtelemtype, is_classtype(ty0), class = `java.lang.Object' .class, tdname+∃(str, class0), interface∃(str0, class2)
Proof step 162:
∃ tys0. # tys0 ≤ # tys1 ∧ contains(str0, ty0 .jtelemtype + (tys0 + mkclasstype(class0))), contains(str0, (ty0 ' + tys1) + mkclasstype(class0) '), mkfs(class1, ty1, fieldvar) ' ∈ instfields(class2), ty0 ≤ ty1, same-subclasses-contains(class, str, str0), tdname+∃(str0, class), class2 ≤ class, tdname+∃(str0, class2), ∀ class0, str0, str, class, tys0. # tys0 < # (ty0 + tys1) → (same-subclasses-contains(class, str, str0) ∧ contains(str0, mkclasstype(class) ' + tys0 + mkclasstype(class0) ') → tdname+∃(str, class0)) ⊦ is_classtype(ty0), class = `java.lang.Object' .class, tdname+∃(str, class0), interface∃(str0, class2)

Rule argument

[LEMMAARG : contains-array-elemtype-ex, [str, ty, tys, class] → [str0, ty0, tys1, class0]]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (str0, ty0, tys1, class0)]]