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Proof step 165 from proof putarray-addarray-01 (previous step)

0 ≤ n→i(# vals) + i, 0 ≤ j, 0 ≤ i, i ≤ j, j ≤ n→i(# vals) + i, i0 < 0 ∨ j ≤ i0, i0 < i ∨ n→i(# vals) + i ≤ i0 ⊦ st[r -- i0 '] = (addarray(r, ty, mklist(initial_value(ty), i→n(i)) + vals, st)[r -- i0 ']), ¬ i0 < 0 ∧ ¬ i + n→i(# vals) ≤ i0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 161:
⊦ i < 0 → (addarray(r, ty, vals, st)[r -- i ']) = st[r -- i ']
Proof step 164:
¬ i0 < 0, 0 ≤ n→i(# vals) + i, 0 ≤ j, 0 ≤ i, i ≤ j, j ≤ n→i(# vals) + i, i0 < 0 ∨ j ≤ i0, i0 < i ∨ n→i(# vals) + i ≤ i0 ⊦ st[r -- i0 '] = (addarray(r, ty, mklist(initial_value(ty), i→n(i)) + vals, st)[r -- i0 ']), ¬ i0 < 0 ∧ ¬ i + n→i(# vals) ≤ i0

Rule argument

[crewrite-arg: add-at-neg , F , [i, st, vals, ty, r] → [i0, st, mklist(initial_value(ty), i→n(i)) + vals, ty, r] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (i0, st, mklist(initial_value(ty), i→n(i)) + vals, ty, r)]]