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Proof step 28 from proof okarray-union (previous step)

st0[r -- _length] = intval(i), r -- _length ∈ st0, 0 ≤ i, r ∈ st0 ⊦ r = jvmref, r -- _type ∈ st0 ∧ is_typevalue(st0[r -- _type]) ∧ is_arraytype(st0[r -- _type] .type) ∧ st0[r -- _type] .type .type ≤ ty ∧ is_arrayref(r, i, st ∪ st0) ∧ (∀ j. ¬ j < 0 ∧ ¬ i ≤ j → oktype(st0[r -- j '], ty, st ∪ st0)) ↔ okreftype(refval(r), mkarraytype(ty), st0) ∧ is_arrayref(r, i, st0) ∧ (∀ j. 0 ≤ j ∧ j < i → oktype(st0[r -- j '], ty, st0)), r ∈ st .refs

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ 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 27:
st0[r -- _length] = intval(i), r -- _length ∈ st0, 0 ≤ i, r ∈ st0 ⊦ r = jvmref, r -- _type ∈ st0 ∧ is_typevalue(st0[r -- _type]) ∧ is_arraytype(st0[r -- _type] .type) ∧ st0[r -- _type] .type .type ≤ ty ∧ is_arrayref(r, i, st ∪ st0) ∧ (∀ j. ¬ j < 0 ∧ ¬ i ≤ j → oktype(st0[r -- j '], ty, st ∪ st0)) ↔ 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)) ∧ is_arrayref(r, i, st0) ∧ (∀ j. 0 ≤ j ∧ j < i → oktype(st0[r -- j '], ty, st0)), r ∈ st .refs

Rule argument

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

Additional information

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