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Proof step 13 from proof okarray-put-badfield (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ okarray(r, ty, st) ↔ okreftype(refval(r), mkarraytype(ty), st) ∧ r ≠ jvmref ∧ r -- _length ∈ st ∧ is_integervalue(st[r -- _length]) ∧ 0 ≤ st[r -- _length] .intval ∧ is_arrayref(r, st[r -- _length] .intval, st) ∧ (∀ j. 0 ≤ j ∧ j < st[r -- _length] .intval → oktype(st[r -- j '], ty, st))
Proof step 12:
st[r -- _length] = intval(i), st[r -- _type] = typeval(mkarraytype(ty0)), r ∈ st, ty0 ≤ ty, r -- _type ∈ st, is_arrayref(r, i, st), r -- _length ∈ st, 0 ≤ i, ∀ j. ¬ j < 0 ∧ ¬ i ≤ j → okval(st[r -- j '], ty) ⊦ r = jvmref, fs ' = _type, fs ' = _length, okreftype(refval(r), mkarraytype(ty), st[r -- fs ', val]) ∧ r ≠ jvmref ∧ r -- _length ∈ st[r -- fs ', val] ∧ is_integervalue(st[r -- fs ', val][r -- _length]) ∧ 0 ≤ (st[r -- fs ', val][r -- _length]) .intval ∧ is_arrayref(r, (st[r -- fs ', val][r -- _length]) .intval, st[r -- fs ', val]) ∧ (∀ j. 0 ≤ j ∧ j < (st[r -- fs ', val][r -- _length]) .intval → oktype(st[r -- fs ', val][r -- j '], ty, st[r -- fs ', val]))

Rule argument

[crewrite-arg: okarrayNotNull , F , [st, ty, r] → [st[r -- fs ', val], ty, r] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st[r -- fs ', val], ty, r)]]