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Proof step 23 from proof isarray-update (previous step)

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

User applied rule case distinction

And obtained the following new goals

Proof step 20:
st[r -- _length] = intval(i), st[r -- _type] = typeval(mkarraytype(ty)), is_arrayref(r, i, update(r0, fis, st)), r -- _type ∈ st, r ∈ st, r -- _length ∈ st, 0 ≤ i, ∀ j. ¬ j < 0 ∧ ¬ i ≤ j → okval(st[r -- j '], ty) ⊦ is_arrayref(r, i, st), r = jvmref, r = r0
Proof step 22:
st[r -- _length] = intval(i), st[r -- _type] = typeval(mkarraytype(ty)), is_arrayref(r, i, update(r0, fis, st)), r -- _type ∈ st, r ∈ st, r -- _length ∈ st, 0 ≤ i, ∀ j. ¬ j < 0 ∧ ¬ i ≤ j → okval(st[r -- j '], ty) ⊦ 0 ≤ j ∧ j < i → okval(st[r -- j '], ty), r = jvmref, r = r0

Rule argument

[CASEDARG : pos: right 3, ()]

Additional information

[[CONCRETESIMPRULES : ()]]