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Proof step 176 from proof addarray-put-01 (previous step)

i→n(i) = n + i→n(j), 1 < i0 + j, 1 < i, 0 < i, i ≤ j + i0, 0 ≤ i, i ≤ i0 + j, 0 < j, 0 ≤ i0 + j, 0 ≤ i0, 0 < i0, j < i ⊦ initial_value(ty) = (val ' + mklist(initial_value(ty), i→n(i0)))[n], j = 0, i = j

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 158:
⊦ n < # vals → (vals + vals0)[n] = vals[n]
Proof step 175:
¬ n < # val ', i→n(i) = n + i→n(j), 1 < i0 + j, 1 < i, 0 < i, i ≤ j + i0, 0 ≤ i, i ≤ i0 + j, 0 < j, 0 ≤ i0 + j, 0 ≤ i0, 0 < i0, j < i ⊦ initial_value(ty) = (val ' + mklist(initial_value(ty), i→n(i0)))[n], j = 0, i = j

Rule argument

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

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ # val ' = 0 +1], [CSIMPSEQ : ⊦ m < 1 ↔ m = 0], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ 0 + m = m], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ i→n(i) = i→n(j) ↔ abs(i) = abs(j)], [CSIMPSEQ : ⊦ 1 < i → abs(i) = i], [CSIMPSEQ : ⊦ 0 < j → abs(j) = j])], [EXTRATERMS : (n, mklist(initial_value(ty), i→n(i0)), val ')]]