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Proof step 77 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), same-subclasses-contains(class3, str, str0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 51:
⊦ same-subclasses-contains(class, str, str0) ↔ same-subclasses(class, str, str0) ∧ (∀ class0. contains(str0, mkclasstype(class), mkclasstype(class0)) → same-subclasses(class0, str, str0))
Proof step 76:
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), same-subclasses(class3, str, str0) ∧ (∀ class0. contains(str0, mkclasstype(class3), mkclasstype(class0)) → same-subclasses(class0, str, str0))

Rule argument

[crewrite-arg: same-subclasses-all-def , F , [str0, str, class] → [str0, str, class3] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (str0, str, class3)]]