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Proof step 39 from proof get-add-02 (previous step)

0 ≤ i, i + j ≤ n→i(# vals), 0 < j, ∀ ty, st, r, vals, i, j0. i→n(j0) < i→n(j) → ( i + j0 ≤ n→i(# vals) ∧ 0 ≤ i ∧ 0 ≤ j0 → getarray(r, i, j0, addarray(r, vals, 0, st[r -- _type, typeval(mkarraytype(ty))][r -- _length, intval(n→i(# vals))])) = sublist(i→n(i), i→n(j0), vals)) ⊦ getarray(r, i, j, addarray(r, vals, 0, st[r -- _type, typeval(mkarraytype(ty))][r -- _length, intval(n→i(# vals))])) = sublist(i→n(i), i→n(j), vals), 0 = j

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ 1 < j → getarray(r, i, j, st) = getarray(r, i, j - 1, st) + st[r -- (i + j - 1) ']
Proof step 18:
¬ 1 < j, 0 ≤ i, i + j ≤ n→i(# vals), 0 < j, ∀ ty, st, r, vals, i, j0. i→n(j0) < i→n(j) → ( i + j0 ≤ n→i(# vals) ∧ 0 ≤ i ∧ 0 ≤ j0 → getarray(r, i, j0, addarray(r, vals, 0, st[r -- _type, typeval(mkarraytype(ty))][r -- _length, intval(n→i(# vals))])) = sublist(i→n(i), i→n(j0), vals)) ⊦ getarray(r, i, j, addarray(r, vals, 0, st[r -- _type, typeval(mkarraytype(ty))][r -- _length, intval(n→i(# vals))])) = sublist(i→n(i), i→n(j), vals), 0 = j
Proof step 38:
1 < j, 0 ≤ i, i + j ≤ n→i(# vals), 0 < j, ∀ ty, st, r, vals, i, j0. i→n(j0) < i→n(j) → ( i + j0 ≤ n→i(# vals) ∧ 0 ≤ i ∧ 0 ≤ j0 → getarray(r, i, j0, addarray(r, vals, 0, st[r -- _type, typeval(mkarraytype(ty))][r -- _length, intval(n→i(# vals))])) = sublist(i→n(i), i→n(j0), vals)) ⊦ getarray(r, i, j - 1, addarray(r, vals, 0, st[r -- _type, typeval(mkarraytype(ty))][r -- _length, intval(n→i(# vals))])) + (addarray(r, vals, 0, st[r -- _type, typeval(mkarraytype(ty))][r -- _length, intval(n→i(# vals))])[r -- (i + j - 1) ']) = sublist(i→n(i), i→n(j), vals), 0 = j

Rule argument

[speclemmaarg: , 1 < j → getarray(r, i, j, st) = getarray(r, i, j - 1, st) + st[r -- (i + j - 1) '] ,[st, j, i, r] → [addarray (r, vals, 0, st[r -- _type, typeval(mkarraytype(ty))] [r -- _length, intval(n→i(# vals)) ]), j, i, r] ,F ,storearrays , ,getArray-rec ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (addarray (r, vals, 0, st[r -- _type, typeval(mkarraytype(ty))] [r -- _length, intval(n→i(# vals)) ]), j, i, r)]]