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Proof step 30 from proof validref-subspec-samesubclasses (previous step)

st[r -- _type] = typeval(mkarraytype(ty0)), ty0 .jtelemtype .class ≤ `java.lang.Object' .class, r ∈ st, same-subclasses(`java.lang.Object' .class, str, str0), junkref(str, r, st), r -- _type ∈ st, has_classtype(ty0), contains(str0, ty0 .jtelemtype, mkclasstype(class)) ⊦ r = jvmref, junkref(str0, r, st), same-subclasses(class, str, str0), contains(str0, mkclasstype(`java.lang.Object' .class), mkclasstype(class))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 22:
⊦ contains(str, ty, ty1) ∧ ty ≤ ty0 ∧ type∃(str, ty0) → contains(str, ty0, ty1)
Proof step 29:
¬ ( contains(str0, ty0 .jtelemtype, mkclasstype(class)) ∧ ty0 .jtelemtype ≤ mkclasstype(`java.lang.Object' .class) ∧ type∃(str0, mkclasstype(`java.lang.Object' .class))), st[r -- _type] = typeval(mkarraytype(ty0)), ty0 .jtelemtype .class ≤ `java.lang.Object' .class, r ∈ st, same-subclasses(`java.lang.Object' .class, str, str0), junkref(str, r, st), r -- _type ∈ st, has_classtype(ty0), contains(str0, ty0 .jtelemtype, mkclasstype(class)) ⊦ r = jvmref, junkref(str0, r, st), same-subclasses(class, str, str0), contains(str0, mkclasstype(`java.lang.Object' .class), mkclasstype(class))

Rule argument

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

Additional information

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