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Proof step 69 from proof validrefs-put-notin-03 (previous step)

is_valid_ref(str, r, st[r -- sk, val]), st[r -- _type] .type ≤ ty, is_valid_ref(r, st), is_obj(str, r, st) ∨ is_array(str, r, st) ⊦ r = jvmref, validrefs(str, r ' + r0 ' + refs1, ty, st[r -- sk, val]) ↔ validrefs(str, r ' + r0 ' + refs1, ty, st), sk = _length, sk = _type, r0 = st[r -- sk] .refval, val .refval = r0, r = r0, r0 ∈ refs1, dups(refs1), r ∈ refs1

User applied rule case distinction

And obtained the following new goals

Rule argument

[CASEDARG : pos: left 4, ()]

Additional information

[[CONCRETESIMPRULES : ()]]