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Proof step 21 from proof okarray-union (previous step)

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

User applied rule case distinction

And obtained the following new goals

Rule argument

[CASEDARG : pos: right 2, ()]

Additional information

[[CONCRETESIMPRULES : ()]]