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Proof step 47 from proof putarray-addarray-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 41:
⊦ n < # vals → (vals + vals0)[n] = vals[n]
Proof step 46:
¬ n < # vals, 0 ≤ i, 0 ≤ i0 + n→i(# vals), 0 ≤ i0 + i + n→i(# vals), 0 < i0, n→i(n) < n→i(# vals) + i0, 0 < i + n→i(# vals) + i0, 0 < n→i(# vals) + i0, # vals ≤ n, 0 ≤ n→i(n) + i ⊦ initial_value(ty) = (vals + mklist(initial_value(ty), i→n(i0)))[n]

Rule argument

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

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ m ≤ n → (n < m ↔ false)])], [EXTRATERMS : (n, mklist(initial_value(ty), i→n(i0)), vals)]]