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Proof step 19 from proof okarray-addarray-other (previous step)

st[r -- _length] = intval(i), 0 ≤ i, r ∈ st, is_arrayref(r, i, st), r -- _length ∈ st, okreftype(refval(r), mkarraytype(ty), st), ∀ j. ¬ j < 0 ∧ ¬ i ≤ j → oktype(st[r -- j '], ty, st) ⊦ r = jvmref, r = r0, okarray(r, ty, addarray(r0, ty0, vals, st))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ 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 18:
st[r -- _length] = intval(i), 0 ≤ i, r ∈ st, is_arrayref(r, i, st), r -- _length ∈ st, okreftype(refval(r), mkarraytype(ty), st), ∀ j. ¬ j < 0 ∧ ¬ i ≤ j → oktype(st[r -- j '], ty, st) ⊦ r = jvmref, r = r0, okreftype(refval(r), mkarraytype(ty), addarray(r0, ty0, vals, st)) ∧ r ≠ jvmref ∧ r -- _length ∈ addarray(r0, ty0, vals, st) ∧ is_integervalue(addarray(r0, ty0, vals, st)[r -- _length]) ∧ 0 ≤ (addarray(r0, ty0, vals, st)[r -- _length]) .intval ∧ is_arrayref(r, (addarray(r0, ty0, vals, st)[r -- _length]) .intval, addarray(r0, ty0, vals, st)) ∧ (∀ j. 0 ≤ j ∧ j < (addarray(r0, ty0, vals, st)[r -- _length]) .intval → oktype(addarray(r0, ty0, vals, st)[r -- j '], ty, addarray(r0, ty0, vals, st)))

Rule argument

[speclemmaarg: , 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)) ,[st, ty, r] → [addarray(r0, ty0, vals, st), ty, r] ,F ,okfuns , ,okarrayNotNull ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (addarray(r0, ty0, vals, st), ty, r)]]