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Proof step 105 from proof putarray-addarray-override (previous step)

i0 < i ∨ n→i(# vals) + i ≤ i0, 0 ≤ i, i + n→i(# vals) ≤ n→i(# vals0), i0 < 0 ∨ i + n→i(# vals) + n→i(# restn(i→n(i) + # vals, vals0)) ≤ i0 ⊦ (addarray(r0, ty, vals0, st)[r0 -- i0 ']) = st[r0 -- i0 '], ¬ i0 < 0 ∧ ¬ i + n→i(# vals) + n→i(# restn(i→n(i) + # vals, vals0)) ≤ i0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 69:
0 ≤ i, i < n→i(# vals) ⊦ (addarray(r, ty, vals, st)[r -- ((* i)) ']) = vals[i→n(i)]
Proof step 95:
¬ (0 ≤ i0 ∧ i0 < n→i(# vals0)), i0 < i ∨ n→i(# vals) + i ≤ i0, 0 ≤ i, i + n→i(# vals) ≤ n→i(# vals0), i0 < 0 ∨ i + n→i(# vals) + n→i(# restn(i→n(i) + # vals, vals0)) ≤ i0 ⊦ (addarray(r0, ty, vals0, st)[r0 -- i0 ']) = st[r0 -- i0 '], ¬ i0 < 0 ∧ ¬ i + n→i(# vals) + n→i(# restn(i→n(i) + # vals, vals0)) ≤ i0
Proof step 104:
0 ≤ i0 ∧ i0 < n→i(# vals0), i0 < i ∨ n→i(# vals) + i ≤ i0, 0 ≤ i, i + n→i(# vals) ≤ n→i(# vals0), i0 < 0 ∨ i + n→i(# vals) + n→i(# restn(i→n(i) + # vals, vals0)) ≤ i0 ⊦ vals0[i→n(i0)] = st[r0 -- i0 '], ¬ i0 < 0 ∧ ¬ i + n→i(# vals) + n→i(# restn(i→n(i) + # vals, vals0)) ≤ i0

Rule argument

[crewrite-arg: add-at-ok-01 , F , [i, st, vals, ty, r] → [i0, st, vals0, ty, r0] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (i0, st, vals0, ty, r0)]]