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Proof step 16 from proof okarray-put-okval-01 (previous step)

st[r0 -- _type] = typeval(mkarraytype(ty0)), st[r0 -- _length] = intval(j), r0 ∈ st, 0 ≤ j, r0 -- _length ∈ st, ty0 ≤ ty, r0 -- _type ∈ st, okval(val0, ty), is_arrayref(r0, j, st), r0 ≠ r ∨ j0 ≠ i, ∀ j0. ¬ j0 < 0 ∧ ¬ j ≤ j0 → okval(st[r0 -- j0 '], ty) ⊦ r0 = jvmref, is_arrayref(r0, j, st[r -- i ', val0]) ∧ (0 ≤ j0 ∧ j0 < j → okval(st[r -- i ', val0][r0 -- j0 '], ty))

User applied rule case distinction

And obtained the following new goals

Proof step 15:
st[r0 -- _type] = typeval(mkarraytype(ty0)), st[r0 -- _length] = intval(j), r0 ∈ st, 0 ≤ j, r0 -- _length ∈ st, ty0 ≤ ty, r0 -- _type ∈ st, okval(val0, ty), is_arrayref(r0, j, st), r0 ≠ r ∨ j0 ≠ i, ∀ j0. ¬ j0 < 0 ∧ ¬ j ≤ j0 → okval(st[r0 -- j0 '], ty) ⊦ 0 ≤ j0 ∧ j0 < j → okval(st[r -- i ', val0][r0 -- j0 '], ty), r0 = jvmref

Rule argument

[CASEDARG : pos: right 2, ()]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_arrayref(r, i, st) → is_arrayref (r, i, st[r -- j ', val])], [CSIMPSEQ : ⊦ r ≠ r0 → ( is_arrayref (r, i, st[r0 -- sk, val0]) ↔ is_arrayref(r, i, st))])]]