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Proof step 38 from proof same-subclasses-forward (previous step)

ty .jtelemtype = mkclasstype(`java.lang.Object' .class), ty0 .jtelemtype .class ≤ `java.lang.Object' .class, same-subclasses(`java.lang.Object' .class, str, str0), contains(str0, ty, mkarraytype(ty0)), has_classtype(ty), ty1 ≤ ty, type∃(str0, ty0), type∃(str0, ty1), type∃(str0, ty), is_reftype(ty), has_classtype(ty0), contains(str0, ty0 .jtelemtype, mkclasstype(class0)), is_classtype(ty1) → ¬ interface∃(str0, ty1 .class) ∧ mkfs(class, ty2, fieldvar) ' ∈ instfields(ty1 .class) ∧ mkarraytype(ty0) ≤ ty2, is_arraytype(ty1) → mkarraytype(ty0) ≤ ty1 .type ⊦ contains(str0, mkclasstype(`java.lang.Object' .class), ty0 .jtelemtype), same-subclasses(class0, str, str0), contains(str0, mkclasstype(`java.lang.Object' .class), mkclasstype(class0))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 33:
⊦ contains(str, ty, ty1) ∧ ty ≤ ty0 ∧ type∃(str, ty0) → contains(str, ty0, ty1)
Proof step 37:
¬ ( contains(str0, ty0 .jtelemtype, mkclasstype(class0)) ∧ ty0 .jtelemtype ≤ mkclasstype(`java.lang.Object' .class) ∧ type∃(str0, mkclasstype(`java.lang.Object' .class))), ty .jtelemtype = mkclasstype(`java.lang.Object' .class), ty0 .jtelemtype .class ≤ `java.lang.Object' .class, same-subclasses(`java.lang.Object' .class, str, str0), contains(str0, ty, mkarraytype(ty0)), has_classtype(ty), ty1 ≤ ty, type∃(str0, ty0), type∃(str0, ty1), type∃(str0, ty), is_reftype(ty), has_classtype(ty0), contains(str0, ty0 .jtelemtype, mkclasstype(class0)), is_classtype(ty1) → ¬ interface∃(str0, ty1 .class) ∧ mkfs(class, ty2, fieldvar) ' ∈ instfields(ty1 .class) ∧ mkarraytype(ty0) ≤ ty2, is_arraytype(ty1) → mkarraytype(ty0) ≤ ty1 .type ⊦ contains(str0, mkclasstype(`java.lang.Object' .class), ty0 .jtelemtype), same-subclasses(class0, str, str0), contains(str0, mkclasstype(`java.lang.Object' .class), mkclasstype(class0))

Rule argument

[crewrite-arg: contains-supertype-04 , F , [str, ty, ty1, ty0] → [str0, ty0 .jtelemtype, mkclasstype(class0), mkclasstype(`java.lang.Object' .class)] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (str0, ty0 .jtelemtype, mkclasstype(class0), mkclasstype(`java.lang.Object' .class))]]