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Proof step 46 from proof same-subclasses-01 (previous step)

contains(str0, (ty0 ' + tys1) + mkclasstype(class0) '), type∃(str0, ty), ty ≤ mkclasstype(`java.lang.Object' .class), same-subclasses(`java.lang.Object' .class, str, str0), is_arraytype(ty) → ty0 ≤ ty .type, is_classtype(ty) → ¬ interface∃(str0, ty .class) ∧ mkfs(class1, ty1, fieldvar) ' ∈ instfields(ty .class) ∧ ty0 ≤ ty1, ∀ class0. contains(str0, mkclasstype(`java.lang.Object' .class), mkclasstype(class0)) → same-subclasses(class0, str, str0), ∀ 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 45:
⊦ ¬ type∃(str, ty) → ¬ contains(str, tys + ty ')

Rule argument

[crewrite-arg: contains-typeex-05 , F , [ty, tys, str] → [mkclasstype(class0), ty0 ' + tys1, str0] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ type∃(str, mkclasstype(class)) ↔ tdname+∃(str, class)], [CSIMPSEQ : ⊦ ¬ tdname+∃(str, class0) ∧ tdname+∃(str0, class0) → ¬ same-subclasses (`java.lang.Object' .class, str, str0)])], [EXTRATERMS : (mkclasstype(class0), ty0 ' + tys1, str0)]]