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Proof step 38 from proof okarray-onlymod (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ 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 37:
onlyModified(r0, st, st0), okreftype(refval(r), mkarraytype(ty), st) ∧ refval(r) .refval ≠ jvmref ∧ (refval(r) .refval -- _length) × intval(st[r -- _length] .intval) ∈ st ∧ 0 ≤ st[r -- _length] .intval ∧ is_arrayref(refval(r) .refval, st[r -- _length] .intval, st) ∧ (∀ j. 0 ≤ j ∧ j < st[r -- _length] .intval → oktype(st[refval(r) .refval -- j '], ty, st)) ⊦ r = r0, r = jvmref, okreftype(refval(r), mkarraytype(ty), st0) ∧ r -- _length ∈ st0 ∧ st0[r -- _length] = intval(st[r -- _length] .intval) ∧ ¬ st[r -- _length] .intval < 0 ∧ is_arrayref(r, st[r -- _length] .intval, st0) ∧ (0 ≤ j ∧ j < st[r -- _length] .intval → okval(st0[r -- j '], ty))

Rule argument

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

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, st[r -- _length] .intval, ty, refval(r))]]