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Proof step 79 from proof same-subclasses-01 (previous step)

same-subclasses-contains(class, str, str0), tdname+∃(str0, class), class2 ≤ class, tdname+∃(str0, class2), contains(str0, (mkclasstype(class3) ' + tys1) + mkclasstype(class0) '), mkfs(class1, mkclasstype(class4), fieldvar) ' ∈ instfields(class2), class3 ≤ class4, ∀ class0, str0, str, class, tys0. # tys0 < # (mkclasstype(class3) + tys1) → (same-subclasses-contains(class, str, str0) ∧ contains(str0, mkclasstype(class) ' + tys0 + mkclasstype(class0) ') → tdname+∃(str, class0)) ⊦ class = `java.lang.Object' .class, tdname+∃(str, class0), interface∃(str0, class2)

User applied rule apply induction

And obtained the following new goals

Proof step 78:
same-subclasses-contains(class, str, str0), tdname+∃(str0, class), class2 ≤ class, tdname+∃(str0, class2), contains(str0, (mkclasstype(class3) ' + tys1) + mkclasstype(class0) '), mkfs(class1, mkclasstype(class4), fieldvar) ' ∈ instfields(class2), class3 ≤ class4, ∀ class0, str0, str, class, tys0. # tys0 < # (mkclasstype(class3) + tys1) → (same-subclasses-contains(class, str, str0) ∧ contains(str0, mkclasstype(class) ' + tys0 + mkclasstype(class0) ') → tdname+∃(str, class0)) ⊦ same-subclasses-contains(class3, str, str0) ∧ contains(str0, mkclasstype(class3) ' + tys1 + mkclasstype(class0) '), class = `java.lang.Object' .class, tdname+∃(str, class0), interface∃(str0, class2)

Rule argument

[substlist-arg: [class0, str0, str, class, tys0] → [class0, str0, str, class3, tys1] ]

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 : ⊦ ¬ n < n], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m + n = n + m])], [EXTRATERMS : (class0, str0, str, class3, tys1)]]