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Proof step 10 from proof okarray-put-07 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ 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 9:
st[r0 -- _length] = intval(i), st[r0 -- _type] = typeval(mkarraytype(ty0)), 0 ≤ i, r0 -- _type ∈ st, ty0 ≤ ty, r0 -- _length ∈ st, is_arrayref(r0, i, st), r0 ∈ st, ∀ j. ¬ j < 0 ∧ ¬ i ≤ j → okval(st[r0 -- j '], ty) ⊦ r0 = jvmref, r = r0, is_referencevalue(refval(r0)) ∧ ( refval(r0) .refval ≠ jvmref → refval(r0) .refval -- _type ∈ st ∧ is_typevalue(st[refval(r0) .refval -- _type]) ∧ st[refval(r0) .refval -- _type] .type ≤ mkarraytype(ty)) ∧ (0 ≤ j ∧ j < i → okval(st[r0 -- j '], ty))

Rule argument

[crewrite-arg: okreftype , F , [st, ty, val] → [st, mkarraytype(ty), refval(r0)] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, mkarraytype(ty), refval(r0))]]