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Proof step 45 from proof getarray-subset (previous step)

st[r -- _type] = typeval(mkarraytype(ty)), r ∈ st, n < # getarray(r, st0), st ⊆ st0, okarray(r, ty, st), r -- _type ∈ st, r -- _length ∈ st, n < i→n(st0[r -- _length] .intval), 0 < st0[r -- _length] .intval, r ∈ st0, okarray(r, ty, st0) ⊦ r = jvmref, noval = st0[r -- n→i(n) '], st0[r -- _length] .intval = 0, getarray(r, st0) = [], r -- n→i(n) ' ∈ st

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 20:
⊦ 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 44:
st[r -- _type] = typeval(mkarraytype(ty)), r ∈ st, n < # getarray(r, st0), st ⊆ st0, okarray(r, ty, st), r -- _type ∈ st, r -- _length ∈ st, n < i→n(st0[r -- _length] .intval), 0 < st0[r -- _length] .intval, r ∈ st0, okreftype(refval(r), mkarraytype(ty), st0) ∧ r ≠ jvmref ∧ r -- _length ∈ st0 ∧ is_integervalue(st0[r -- _length]) ∧ 0 ≤ st0[r -- _length] .intval ∧ is_arrayref(r, st0[r -- _length] .intval, st0) ∧ (∀ j. 0 ≤ j ∧ j < st0[r -- _length] .intval → oktype(st0[r -- j '], ty, st0)) ⊦ r = jvmref, noval = st0[r -- n→i(n) '], st0[r -- _length] .intval = 0, getarray(r, st0) = [], r -- n→i(n) ' ∈ st

Rule argument

[crewrite-arg: okarrayNotNull, F, [st, ty, r] → [st0, ty, r]]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st0, ty, r)]]