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Proof step 64 from proof validrefs-put-notin-03 (previous step)

is_array(str, r, st), is_valid_ref(r, st), is_array(str, r, st[r -- sk, val]), st[r -- _type] .type ≤ ty ⊦ sk = _length, sk = _type, r0 = st[r -- sk] .refval, val .refval = r0, r = r0, r = jvmref, (∃ i. 0 ≤ i ∧ i < st[r -- _length] .intval ∧ is_referencevalue(st[r -- sk, val][r -- i ']) ∧ r0 = (st[r -- sk, val][r -- i ']) .refval ∧ validrefs(str, (st[r -- sk, val][r -- i ']) .refval ' + refs1, st[r -- _type] .type .type, st[r -- sk, val])) ↔ (∃ i. ¬ i < 0 ∧ ¬ st[r -- _length] .intval ≤ i ∧ is_referencevalue(st[r -- i ']) ∧ r0 = st[r -- i '] .refval ∧ validrefs(str, st[r -- i '] .refval ' + refs1, st[r -- _type] .type .type, st)), r0 ∈ refs1, dups(refs1), r ∈ refs1

User applied rule case distinction

And obtained the following new goals

Rule argument

[CASEDARG : pos: right 7, ()]

Additional information

[[CONCRETESIMPRULES : ()]]