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Proof step 23 from proof same-subclasses-array-forward (previous step)

st[r -- i '] = refval(r0), st[r -- _type] .type = mkarraytype(ty), 0 < st[r -- _length] .intval, 0 ≤ i, has_classtype(st[r0 -- _type] .type), i < st[r -- _length] .intval, is_array(str0, r, st), same-subclasses(ty .jtelemtype .class, str, str0), is_array(str, r, st), has_classtype(ty), ∀ class0. contains(str0, ty .jtelemtype, mkclasstype(class0)) → same-subclasses(class0, str, str0) ⊦ ty .jtelemtype = mkclasstype(`java.lang.Object' .class), r0 = jvmref, r = jvmref, st[r0 -- _type] .type .jtelemtype ≤ ty .jtelemtype, contains(str0, ty .jtelemtype, st[r0 -- _type] .type .jtelemtype), junkref(str0, r, st), contains(str0, mkarraytype(ty), st[r0 -- _type] .type), same-subclasses(st[r0 -- _type] .type .jtelemtype .class, str, str0) ∧ (contains(str0, st[r0 -- _type] .type .jtelemtype, mkclasstype(class)) → same-subclasses(class, str, str0))

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

[speclemmaarg: , is_array(str, r, st) → ( junkref(str, r, st) ↔ (∃ i. 0 ≤ i ∧ i < st[r -- _length] .intval ∧ is_referencevalue(st[r -- i ']) ∧ st[r -- i '] .refval ≠ jvmref ∧ ( ¬ st[st[r -- i '] .refval -- _type] .type ≤ st[r -- _type] .type .type ∨ junkref(str, st[r -- i '] .refval, st)))) ,[st, r, str] → [st, r, str0] ,F ,junkrefs , ,junkref-array ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, r, str0)]]