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Proof step 143 from proof putarray-addarray-override (previous step)

n→i(n) + i < n→i(# vals0), 0 ≤ i, i→n(i) < # vals0, i→n(i) + # vals ≤ # vals0, i→n(i) + n < # vals0, 0 ≤ n→i(n) + i, # vals ≤ n ⊦ vals0 = [], vals0[i→n(i) + n] = (vals + restn(i→n(i) + # vals, vals0))[n]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 130:
⊦ n < # vals → (vals + vals0)[n] = vals[n]
Proof step 142:
¬ n < # vals, n→i(n) + i < n→i(# vals0), 0 ≤ i, i→n(i) < # vals0, i→n(i) + # vals ≤ # vals0, i→n(i) + n < # vals0, 0 ≤ n→i(n) + i, # vals ≤ n ⊦ vals0 = [], vals0[i→n(i) + n] = (vals + restn(i→n(i) + # vals, vals0))[n]

Rule argument

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

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ m ≤ n → (n < m ↔ false)])], [EXTRATERMS : (n, restn(i→n(i) + # vals, vals0), vals)]]