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Proof step 71 from proof same-subclasses-array-forward (previous step)

st[r0 -- _type] .type = mkarraytype(ty0), ty .jtelemtype = mkclasstype(`java.lang.Object' .class), st[r -- i '] = refval(r0), st[r -- _type] .type = mkarraytype(ty), is_array(str0, r0, st), mkarraytype(ty0) ≤ ty, is_array(str0, r, st), has_classtype(ty0), 0 ≤ i, 0 < st[r -- _length] .intval, has_classtype(ty), is_array(str, r, st), same-subclasses(`java.lang.Object' .class, str, str0), i < st[r -- _length] .intval, type∃(str0, ty0), ∀ class0. contains(str0, mkclasstype(`java.lang.Object' .class), mkclasstype(class0)) → same-subclasses(class0, str, str0) ⊦ r = jvmref, r0 = jvmref, junkref(str0, r0, st), type∃(str0, ty0 .jtelemtype)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 67:
⊦ type∃(str, ty) ↔ ¬ has_classtype(ty) ∨ tdname+∃(str, ty .jtclass)
Proof step 70:
st[r0 -- _type] .type = mkarraytype(ty0), ty .jtelemtype = mkclasstype(`java.lang.Object' .class), st[r -- i '] = refval(r0), st[r -- _type] .type = mkarraytype(ty), is_array(str0, r0, st), mkarraytype(ty0) ≤ ty, is_array(str0, r, st), has_classtype(ty0), 0 ≤ i, 0 < st[r -- _length] .intval, has_classtype(ty), is_array(str, r, st), same-subclasses(`java.lang.Object' .class, str, str0), i < st[r -- _length] .intval, ¬ has_classtype(ty0) ∨ tdname+∃(str0, ty0 .jtclass), ∀ class0. contains(str0, mkclasstype(`java.lang.Object' .class), mkclasstype(class0)) → same-subclasses(class0, str, str0) ⊦ r = jvmref, r0 = jvmref, junkref(str0, r0, st), type∃(str0, ty0 .jtelemtype)

Rule argument

[speclemmaarg: ,type∃(str, ty) ↔ ¬ has_classtype(ty) ∨ tdname+∃(str, ty .jtclass) ,[ty, str] → [ty0, str0] ,F ,typefuns , ,typeex-def ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (ty0, str0)]]