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Proof step 18 from proof okarray-addarray-other (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
⊦ r ≠ r0 → (okreftype(refval(r), ty, addarray(r0, ty0, vals, st)) ↔ okreftype(refval(r), ty, st))
Proof step 4:
⊦ r ≠ r0 → (r -- sk ∈ addarray(r0, ty, vals, st) ↔ r -- sk ∈ st)
Proof step 5:
⊦ r ≠ r0 → (addarray(r, ty, vals, st)[r0 -- sk]) = st[r0 -- sk]
Proof step 6:
⊦ r ≠ r0 → (is_arrayref(r, i, addarray(r0, ty0, vals, st)) ↔ is_arrayref(r, i, st))
Proof step 17:
st[r -- _length] = intval(i), okreftype(refval(r), mkarraytype(ty), st), r -- _length ∈ st, is_arrayref(r, i, st), r ∈ st, 0 ≤ i, j < i, 0 ≤ j, 0 < i, ∀ j. ¬ j < 0 ∧ ¬ i ≤ j → oktype(st[r -- j '], ty, st) ⊦ r = r0, r = jvmref, oktype(st[r -- j '], ty, addarray(r0, ty0, vals, st))

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPFORWARD : ⊦ i < j ∧ 0 ≤ i → 0 < j], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)], [CSIMPSEQ : ⊦ intval(i) .intval = i], [CSIMPSEQ : ⊦ is_integervalue(intval(i))], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i])]]