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Proof step 81 from proof putarray-addarray-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 68:
⊦ ¬ n < # vals → (vals + vals0)[n] = vals0[n - # vals]
Proof step 80:
¬ i→n(i2 + i) < # mklist(initial_value(ty), i→n(i)), 0 ≤ i2, 0 ≤ i2 + i, i2 < n→i(# vals), 0 ≤ i, 0 ≤ i0 + n→i(# vals), 0 ≤ i0 + i + n→i(# vals), 0 < i0, 0 < n→i(# vals) + i, i2 < n→i(# vals) + i0, 0 < n→i(# vals) + i0 ⊦ vals = [], vals[i→n(i2)] = (vals + mklist(initial_value(ty), i→n(i0)))[i→n(i2 + i) - # mklist(initial_value(ty), i→n(i))]

Rule argument

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

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ n < # vals → (vals + vals0)[n] = vals[n]], [CSIMPSEQ : ⊦ (vals + vals0) + vals1 = vals + vals0 + vals1], [CSIMPSEQ : ⊦ # mklist(val, n) = n], [CSIMPSEQ : ⊦ i→n(i) < i→n(j) ↔ abs(i) < abs(j)], [CSIMPSEQ : ⊦ 0 ≤ i ∧ 0 ≤ j → abs(i + j) = abs(i) + abs(j)], [CSIMPSEQ : ⊦ 0 ≤ i → abs(i) = i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i + j < j ↔ i < 0], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)])], [EXTRATERMS : (i→n(i2 + i), vals + mklist(initial_value(ty), i→n(i0)), mklist(initial_value(ty), i→n(i)))]]