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Proof step 161 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), # tys ≤ # tys1, contains(str0, ty0 .jtelemtype ' + 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, is_classtype(ty0), tdname+∃(str, class0), interface∃(str0, class2)

User applied rule apply induction

And obtained the following new goals

Proof step 160:
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), # tys ≤ # tys1, contains(str0, ty0 .jtelemtype ' + 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)) ⊦ same-subclasses-contains(ty0 .jtelemtype .class, str, str0) ∧ contains(str0, mkclasstype(ty0 .jtelemtype .class) ' + tys + mkclasstype(class0) '), class = `java.lang.Object' .class, is_classtype(ty0), tdname+∃(str, class0), interface∃(str0, class2)

Rule argument

[substlist-arg: [class0, str0, str, class, tys0] → [class0, str0, str, ty0 .jtelemtype .class, tys] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ty + tys = ty ' + tys], [CSIMPSEQ : ⊦ # (tys + tys0) = # tys + # tys0], [CSIMPSEQ : ⊦ # ty ' = 0 +1], [CSIMPSEQ : ⊦ (tys + tys0) + tys1 = tys + tys0 + tys1], [CSIMPSEQ : ⊦ m < n + 1 ↔ ¬ n < m], [CSIMPSEQ : ⊦ m ≤ n → (n < m ↔ false)], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m + n = n + m])], [EXTRATERMS : (class0, str0, str, ty0 .jtelemtype .class, tys)]]