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Proof step 35 from proof same-subclasses-array-forward (previous step)

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

Proof step 33:
⊦ has_classtype(ty) ↔ is_classtype(ty .jtelemtype)
Proof step 34:
st[r -- i '] = refval(r0), st[r0 -- _type] .type .jtelemtype ≤ st[r -- _type] .type .jtelemtype, is_array(str, r, st), same-subclasses(st[r -- _type] .type .jtelemtype .class, str, str0), i < st[r -- _length] .intval, has_classtype(st[r0 -- _type] .type), 0 ≤ i, 0 < st[r -- _length] .intval, is_classtype(st[r -- _type] .type .jtelemtype), ∀ class0. contains(str0, st[r -- _type] .type .jtelemtype, mkclasstype(class0)) → same-subclasses(class0, str, str0) ⊦ r0 = jvmref, st[r -- _type] .type .jtelemtype = mkclasstype(`java.lang.Object' .class), junkref(str0, r, st), contains(str0, st[r -- _type] .type .jtelemtype, st[r0 -- _type] .type .jtelemtype), st[r0 -- _type] .type .jtelemtype .class ≤ st[r -- _type] .type .jtelemtype .class, same-subclasses(st[r0 -- _type] .type .jtelemtype .class, str, str0) ∧ (contains(str0, st[r0 -- _type] .type .jtelemtype, mkclasstype(class)) → same-subclasses(class, str, str0))

Rule argument

[speclemmaarg: ,has_classtype(ty) ↔ is_classtype(ty .jtelemtype) ,[ty] → [st[r -- _type] .type] ,F ,typefuns , ,has-classtype ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st[r -- _type] .type)]]