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Proof step 48 from proof same-subclasses-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 44:
⊦ 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 47:
same-subclasses(`java.lang.Object' .class, str, str0) ∧ (∀ class0. contains(str0, mkclasstype(`java.lang.Object' .class), mkclasstype(class0)) → same-subclasses(class0, str, str0)), ty ≤ mkclasstype(`java.lang.Object' .class), type∃(str0, ty), contains(str0, (ty0 ' + tys1) + mkclasstype(class0) '), is_classtype(ty) → ¬ interface∃(str0, ty .class) ∧ mkfs(class1, ty1, fieldvar) ' ∈ instfields(ty .class) ∧ ty0 ≤ ty1, is_arraytype(ty) → ty0 ≤ ty .type, ∀ class0, str0, str, class, tys0. # tys0 < # (ty0 + tys1) → (same-subclasses-contains(class, str, str0) ∧ contains(str0, mkclasstype(class) ' + tys0 + mkclasstype(class0) ') → tdname+∃(str, class0)) ⊦ tdname+∃(str, class0)

Rule argument

[crewrite-arg: same-subclasses-all-def , F , [str0, str, class] → [str0, str, `java.lang.Object' .class] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (str0, str, `java.lang.Object' .class)]]