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Proof step 75 from proof putarray-addarray-01 (previous step)

0 < n→i(# vals) + i0, i2 < n→i(# vals) + i0, 0 < n→i(# vals) + i, 0 < i0, 0 ≤ i0 + i + n→i(# vals), 0 ≤ i0 + n→i(# vals), 0 ≤ i, i2 < n→i(# vals), 0 ≤ i2 + i, 0 ≤ i2 ⊦ vals[i→n(i2)] = (vals + mklist(initial_value(ty), i→n(i0)))[i→n(i2)], vals = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 70:
⊦ n < # vals → (vals + vals0)[n] = vals[n]
Proof step 74:
¬ i→n(i2) < # vals, 0 < n→i(# vals) + i0, i2 < n→i(# vals) + i0, 0 < n→i(# vals) + i, 0 < i0, 0 ≤ i0 + i + n→i(# vals), 0 ≤ i0 + n→i(# vals), 0 ≤ i, i2 < n→i(# vals), 0 ≤ i2 + i, 0 ≤ i2 ⊦ vals[i→n(i2)] = (vals + mklist(initial_value(ty), i→n(i0)))[i→n(i2)], vals = []

Rule argument

[speclemmaarg: ,n < # vals → (vals + vals0)[n] = vals[n] ,[n, vals0, vals] → [i→n(i2), mklist(initial_value(ty), i→n(i0)), vals] ,F ,list-del ,javavalues ,get-append-less ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (i→n(i2), mklist(initial_value(ty), i→n(i0)), vals)]]