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Proof step 20 from proof isarray-addarray (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
⊦ okreftype(refval(r), mkarraytype(ty), addarray(r, ty, vals, st))
Proof step 6:
⊦ r -- _length ∈ addarray(r, ty, vals, st)
Proof step 7:
⊦ (addarray(r, ty, vals, st)[r -- _length]) = intval(n→i(# vals))
Proof step 8:
⊦ 0 ≤ i ∧ i < n→i(# vals) → (addarray(r, ty, vals, st)[r -- i ']) = vals[i→n(i)]
Proof step 19:
∀ j. ¬ j < 0 ∧ ¬ n→i(# vals) ≤ j → oktype(vals[i→n(j)], ty, st) ⊦ r = jvmref, is_arrayref(r, n→i(# vals), addarray(r, ty, vals, st)) ∧ (0 ≤ j ∧ j < n→i(# vals) → oktype(vals[i→n(j)], ty, addarray(r, ty, vals, st)))

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ 0 ≤ n→i(n)], [CSIMPSEQ : ⊦ intval(i) .intval = i], [CSIMPSEQ : ⊦ is_integervalue(intval(i))])]]