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Proof step 21 from proof getarray-subset-02 (previous step)

st[r -- _type] = typeval(mkarraytype(ty)), r ∈ st, 0 ≤ i, i + j ≤ st[r -- _length] .intval, okarray(r, ty, st), r -- _type ∈ st, st ⊆ st0 ⊦ r = jvmref, getarray(r, i, j, st) = getarray(r, i, j, st0), is_arrayref(r, i + j, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ 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 20:
st[r -- _type] = typeval(mkarraytype(ty)), r ∈ st, 0 ≤ i, i + j ≤ st[r -- _length] .intval, 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)), r -- _type ∈ st, st ⊆ st0 ⊦ r = jvmref, getarray(r, i, j, st) = getarray(r, i, j, st0), is_arrayref(r, i + j, st)

Rule argument

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

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, ty, r)]]