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Proof step 30 from proof okarray-union (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ okarray(val, ty, i, st) ↔ okreftype(val, mkarraytype(ty), st) ∧ val .refval ≠ jvmref ∧ (val .refval -- _length) × intval(i) ∈ st ∧ 0 ≤ i ∧ is_arrayref(val .refval, i, st) ∧ (∀ j. 0 ≤ j ∧ j < i → oktype(st[val .refval -- j '], ty, st))
Proof step 29:
⊦ r -- _type ∈ st0 ∧ is_typevalue(st0[r -- _type]) ∧ is_arraytype(st0[r -- _type] .type) ∧ st0[r -- _type] .type .type ≤ ty ∧ r ≠ jvmref ∧ r -- _length ∈ st0 ∧ st0[r -- _length] = intval(i) ∧ 0 ≤ i ∧ is_arrayref(r, i, st ∪ st0) ∧ (∀ j. ¬ j < 0 ∧ ¬ i ≤ j → oktype(st0[r -- j '], ty, st ∪ st0)) ↔ okreftype(refval(r), mkarraytype(ty), st0) ∧ refval(r) .refval ≠ jvmref ∧ (refval(r) .refval -- _length) × intval(i) ∈ st0 ∧ 0 ≤ i ∧ is_arrayref(refval(r) .refval, i, st0) ∧ (∀ j. 0 ≤ j ∧ j < i → oktype(st0[refval(r) .refval -- j '], ty, st0)), r ∈ st .refs

Rule argument

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

Additional information

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