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Proof step 52 from proof okarray-union-03 (previous step)

st[r -- _length] = intval(st[r -- _length] .intval), st[r -- _type] = typeval(mkarraytype(ty0)), r -- _length ∈ st, r -- _type ∈ st, r ∈ st, ty0 ≤ ty, is_arrayref(r, st[r -- _length] .intval, st), 0 ≤ st[r -- _length] .intval, ∀ j0. ¬ j0 < 0 ∧ ¬ st[r -- _length] .intval ≤ j0 → oktype(st[r -- j0 '], ty, st) ⊦ r = jvmref, (0 ≤ j ∧ j < st[r -- _length] .intval → oktype((st0 ∪ st)[r -- j '], ty, st0 ∪ st)) ∧ is_arrayref(r, st[r -- _length] .intval, st0 ∪ st)

User applied rule case distinction

And obtained the following new goals

Rule argument

[CASEDARG : pos: right 2, ()]

Additional information

[[CONCRETESIMPRULES : ()]]