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Proof step 178 from proof putarray-addarray-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 174:
⊦ n < # vals → (vals + vals0)[n] = vals[n]
Proof step 177:
i→n(i0) < # mklist(initial_value(ty), i→n(i)), i0 < j, 0 < i, i0 < i, 0 < i + n→i(# vals), 0 ≤ i0, i0 < i + n→i(# vals), j ≤ n→i(# vals) + i, i ≤ j, 0 ≤ i, 0 ≤ j, 0 ≤ n→i(# vals) + i, i0 < n→i(# vals) + i, 0 < j ⊦ initial_value(ty) = (mklist(initial_value(ty), i→n(i))[i→n(i0)])

Rule argument

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

Additional information

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