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Proof step 58 from proof putarray-addarray-01 (previous step)

i ≤ i1, n→i(# vals) + i ≤ i1, 0 ≤ i, 0 ≤ i0 + n→i(# vals), 0 ≤ i0 + i + n→i(# vals), 0 < i0, i1 < i + n→i(# vals) + i0, 0 ≤ i1, 0 < i + n→i(# vals) + i0, 0 < n→i(# vals) + i0 ⊦ initial_value(ty) = (mklist(initial_value(ty), i→n(i)) + vals + mklist(initial_value(ty), i→n(i0)))[i→n(i1)]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 36:
⊦ n < # vals → (vals + vals0)[n] = vals[n]
Proof step 57:
¬ i→n(i1) < # mklist(initial_value(ty), i→n(i)), i ≤ i1, n→i(# vals) + i ≤ i1, 0 ≤ i, 0 ≤ i0 + n→i(# vals), 0 ≤ i0 + i + n→i(# vals), 0 < i0, i1 < i + n→i(# vals) + i0, 0 ≤ i1, 0 < i + n→i(# vals) + i0, 0 < n→i(# vals) + i0 ⊦ initial_value(ty) = (mklist(initial_value(ty), i→n(i)) + vals + mklist(initial_value(ty), i→n(i0)))[i→n(i1)]

Rule argument

[speclemmaarg: ,n < # vals → (vals + vals0)[n] = vals[n] ,[n, vals0, vals] → [i→n(i1), vals + mklist(initial_value(ty), i→n(i0)), mklist(initial_value(ty), i→n(i))] ,F ,list-del ,javavalues ,get-append-less ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ # mklist(val, n) = n], [CSIMPSEQ : ⊦ i→n(i) < i→n(j) ↔ abs(i) < abs(j)], [CSIMPSEQ : ⊦ 0 ≤ i → abs(i) = i], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)])], [EXTRATERMS : (i→n(i1), vals + mklist(initial_value(ty), i→n(i0)), mklist(initial_value(ty), i→n(i)))]]