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Proof step 14 from proof same-subclasses-array-forward (previous step)

st[r -- i '] = refval(r0), 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, ∀ class0. contains(str0, mkclasstype(st[r -- _type] .type .jtelemtype .class), mkclasstype(class0)) → same-subclasses(class0, str, str0) ⊦ r0 = jvmref, has_classtype(st[r -- _type] .type), junkref(str0, r, st), contains(str0, mkclasstype(st[r -- _type] .type .jtelemtype .class), st[r0 -- _type] .type .jtelemtype), 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 9:
⊦ 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))))
Proof step 13:
is_array(str0, r, st), st[r -- i '] = refval(r0), 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, ∀ class0. contains(str0, mkclasstype(st[r -- _type] .type .jtelemtype .class), mkclasstype(class0)) → same-subclasses(class0, str, str0) ⊦ r0 = jvmref, has_classtype(st[r -- _type] .type), ∃ 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(str0, st[r -- i '] .refval, st)), contains(str0, mkclasstype(st[r -- _type] .type .jtelemtype .class), st[r0 -- _type] .type .jtelemtype), 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: , 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 : ([CSIMPSEQ : ⊦ ¬ is_array(str, r, st) ∧ ¬ has_classtype (st[r -- _type] .type) → ¬ is_array(str0, r, st)])], [EXTRATERMS : (st, r, str0)]]