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Proof step 187 from proof putarray-addarray-override (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 111:
⊦ n < # vals → (vals + vals0)[n] = vals[n]
Proof step 164:
¬ i→n(i0) < # firstn(i→n(i), vals0), 0 ≤ i, i + n→i(# vals) ≤ n→i(# vals0), i0 < i + n→i(# vals) + n→i(# restn(i→n(i) + # vals, vals0)), 0 ≤ i0, 0 < i + n→i(# vals) + n→i(# restn(i→n(i) + # vals, vals0)) ⊦ (putArray(vals, r0, i, addarray(r0, ty, vals0, st))[r0 -- i0 ']) = (firstn(i→n(i), vals0) + vals + restn(i→n(i) + # vals, vals0))[i→n(i0)]
Proof step 186:
i→n(i0) < # firstn(i→n(i), vals0), 0 ≤ i, i + n→i(# vals) ≤ n→i(# vals0), i0 < i + n→i(# vals) + n→i(# restn(i→n(i) + # vals, vals0)), 0 ≤ i0, 0 < i + n→i(# vals) + n→i(# restn(i→n(i) + # vals, vals0)) ⊦ (putArray(vals, r0, i, addarray(r0, ty, vals0, st))[r0 -- i0 ']) = (firstn(i→n(i), vals0)[i→n(i0)])

Rule argument

[speclemmaarg: ,n < # vals → (vals + vals0)[n] = vals[n] ,[n, vals0, vals] → [i→n(i0), vals + restn(i→n(i) + # vals, vals0), firstn(i→n(i), vals0)] ,F ,list-del ,javavalues ,get-append-less ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (i→n(i0), vals + restn(i→n(i) + # vals, vals0), firstn(i→n(i), vals0))]]