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Proof step 37 from proof getarray-subset (previous step)

st0[r -- _length] = intval(i), st[r -- _type] = typeval(mkarraytype(ty)), st0[r -- _type] = typeval(mkarraytype(ty0)), r ∈ st0, r -- _length ∈ st0, ty0 ≤ ty, r -- _type ∈ st0, n < i→n(i), r -- _length ∈ st, r -- _type ∈ st, okarray(r, ty, st), st ⊆ st0, n < # getarray(r, st0), r ∈ st, is_arrayref(r, i, st0), 0 < i, ∀ j. ¬ j < 0 ∧ ¬ i ≤ j → oktype(st0[r -- j '], ty, st0) ⊦ r = jvmref, getarray(r, st0) = [], i = 0, noval = st0[r -- n→i(n) '], r -- n→i(n) ' ∈ st

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 22:
⊦ 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 36:
st0[r -- _length] = intval(i), st[r -- _type] = typeval(mkarraytype(ty)), st0[r -- _type] = typeval(mkarraytype(ty0)), r ∈ st0, r -- _length ∈ st0, ty0 ≤ ty, r -- _type ∈ st0, n < i→n(i), r -- _length ∈ st, r -- _type ∈ 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 ⊆ st0, n < # getarray(r, st0), r ∈ st, is_arrayref(r, i, st0), 0 < i, ∀ j. ¬ j < 0 ∧ ¬ i ≤ j → oktype(st0[r -- j '], ty, st0) ⊦ r = jvmref, getarray(r, st0) = [], i = 0, noval = st0[r -- n→i(n) '], r -- n→i(n) ' ∈ st

Rule argument

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

Additional information

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