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Proof step 31 from proof okarray-onlymod (previous step)

st[r -- _length] = intval(st[r -- _length] .intval), st[r -- _type] = typeval(mkarraytype(ty0)), onlyModified(r0, st, st0), r -- _type ∈ st, ty0 ≤ ty, r -- _length ∈ st, is_arrayref(r, st[r -- _length] .intval, st), is_arrayref(r, st[r -- _length] .intval, st0), r ∈ st, 0 ≤ st[r -- _length] .intval, ∀ j0. ¬ j0 < 0 ∧ ¬ st[r -- _length] .intval ≤ j0 → okval(st[r -- j0 '], ty) ⊦ okreftype(refval(r), mkarraytype(ty), st0), r = r0, r = jvmref

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 22:
⊦ okreftype(val, ty, st) ↔ is_referencevalue(val) ∧ (val .refval ≠ jvmref → val .refval -- _type ∈ st ∧ is_typevalue(st[val .refval -- _type]) ∧ st[val .refval -- _type] .type ≤ ty)
Proof step 30:
st[r -- _length] = intval(st[r -- _length] .intval), st[r -- _type] = typeval(mkarraytype(ty0)), onlyModified(r0, st, st0), r -- _type ∈ st, ty0 ≤ ty, r -- _length ∈ st, is_arrayref(r, st[r -- _length] .intval, st), is_arrayref(r, st[r -- _length] .intval, st0), r ∈ st, 0 ≤ st[r -- _length] .intval, ∀ j0. ¬ j0 < 0 ∧ ¬ st[r -- _length] .intval ≤ j0 → okval(st[r -- j0 '], ty) ⊦ is_referencevalue(refval(r)) ∧ ( refval(r) .refval ≠ jvmref → refval(r) .refval -- _type ∈ st0 ∧ is_typevalue(st0[refval(r) .refval -- _type]) ∧ st0[refval(r) .refval -- _type] .type ≤ mkarraytype(ty)), r = r0, r = jvmref

Rule argument

[crewrite-arg: okreftype , F , [st, ty, val] → [st0, mkarraytype(ty), refval(r)] ]

Additional information

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