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Proof step 36 from proof isarray-update (previous step)

st[r -- _type] = typeval(mkarraytype(ty)), st[r -- _length] = intval(i), 0 ≤ i, r -- _length ∈ st, r ∈ st, r -- _type ∈ st ⊦ is_arrayref(r, i, update(r0, fis, st)) ∧ (∀ j. ¬ j < 0 ∧ ¬ i ≤ j → okval(st[r -- j '], ty)) ↔ okreftype(refval(r), mkarraytype(ty), st) ∧ is_arrayref(r, i, st) ∧ (∀ j. 0 ≤ j ∧ j < i → okval(st[r -- j '], ty)), r = r0, r = jvmref

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 12:
⊦ 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 35:
st[r -- _type] = typeval(mkarraytype(ty)), st[r -- _length] = intval(i), 0 ≤ i, r -- _length ∈ st, r ∈ st, r -- _type ∈ st ⊦ is_arrayref(r, i, update(r0, fis, st)) ∧ (∀ j. ¬ j < 0 ∧ ¬ i ≤ j → okval(st[r -- j '], ty)) ↔ is_referencevalue(refval(r)) ∧ ( refval(r) .refval ≠ jvmref → refval(r) .refval -- _type ∈ st ∧ is_typevalue(st[refval(r) .refval -- _type]) ∧ st[refval(r) .refval -- _type] .type ≤ mkarraytype(ty)) ∧ is_arrayref(r, i, st) ∧ (∀ j. 0 ≤ j ∧ j < i → okval(st[r -- j '], ty)), r = r0, r = jvmref

Rule argument

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

Additional information

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