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Proof step 22 from proof okarray-put-okval-01 (previous step)

st[r0 -- _length] = intval(j), st[r0 -- _type] = typeval(mkarraytype(ty0)), is_arrayref(r0, j, st), okval(val0, ty), r0 -- _type ∈ st, ty0 ≤ ty, r0 -- _length ∈ st, 0 ≤ j, r0 ∈ st, ∀ j0. ¬ j0 < 0 ∧ ¬ j ≤ j0 → okval(st[r0 -- j0 '], ty) ⊦ r0 = jvmref, okarray(refval(r0), ty, j, st[r -- i ', val0])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ 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 21:
st[r0 -- _length] = intval(j), st[r0 -- _type] = typeval(mkarraytype(ty0)), is_arrayref(r0, j, st), okval(val0, ty), r0 -- _type ∈ st, ty0 ≤ ty, r0 -- _length ∈ st, 0 ≤ j, r0 ∈ st, ∀ j0. ¬ j0 < 0 ∧ ¬ j ≤ j0 → okval(st[r0 -- j0 '], ty) ⊦ r0 = jvmref, okreftype(refval(r0), mkarraytype(ty), st[r -- i ', val0]) ∧ refval(r0) .refval ≠ jvmref ∧ (refval(r0) .refval -- _length) × intval(j) ∈ st[r -- i ', val0] ∧ 0 ≤ j ∧ is_arrayref(refval(r0) .refval, j, st[r -- i ', val0]) ∧ (∀ j0. 0 ≤ j0 ∧ j0 < j → oktype(st[r -- i ', val0][refval(r0) .refval -- j0 '], ty, st[r -- i ', val0]))

Rule argument

[crewrite-arg: okarrayOfLength , F , [st, i, ty, val] → [st[r -- i ', val0], j, ty, refval(r0)] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st[r -- i ', val0], j, ty, refval(r0))]]