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Proof step 10 from proof okarray-putbar-other (previous step)

st[r -- _length] = intval(i0), st[r -- _type] = typeval(mkarraytype(ty1)), ty1 ≤ ty, is_arrayref(r, i0, putByteArray(bytes, r1, i, st)), r -- _type ∈ st, r -- _length ∈ st, r ∈ st, 0 ≤ i0, ∀ j. ¬ j < 0 ∧ ¬ i0 ≤ j → okval(st[r -- j '], ty) ⊦ r = jvmref, r = r1, is_arrayref(r, i0, st) ∧ (0 ≤ j ∧ j < i0 → okval(st[r -- j '], ty))

User applied rule case distinction

And obtained the following new goals

Proof step 7:
st[r -- _length] = intval(i0), st[r -- _type] = typeval(mkarraytype(ty1)), ty1 ≤ ty, is_arrayref(r, i0, putByteArray(bytes, r1, i, st)), r -- _type ∈ st, r -- _length ∈ st, r ∈ st, 0 ≤ i0, ∀ j. ¬ j < 0 ∧ ¬ i0 ≤ j → okval(st[r -- j '], ty) ⊦ is_arrayref(r, i0, st), r = jvmref, r = r1
Proof step 9:
st[r -- _length] = intval(i0), st[r -- _type] = typeval(mkarraytype(ty1)), ty1 ≤ ty, is_arrayref(r, i0, putByteArray(bytes, r1, i, st)), r -- _type ∈ st, r -- _length ∈ st, r ∈ st, 0 ≤ i0, ∀ j. ¬ j < 0 ∧ ¬ i0 ≤ j → okval(st[r -- j '], ty) ⊦ 0 ≤ j ∧ j < i0 → okval(st[r -- j '], ty), r = jvmref, r = r1

Rule argument

[CASEDARG : pos: right 3, ()]

Additional information

[[CONCRETESIMPRULES : ()]]