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Proof step 83 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 ⊦ vals = [], vals[i→n(i2)] = (addarray(r, ty, mklist(initial_value(ty), i→n(i)) + vals + mklist(initial_value(ty), i→n(i0)), st)[r -- (i2 + i) '])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 67:
⊦ 0 ≤ i ∧ i < n→i(# vals) → (addarray(r, ty, vals, st)[r -- i ']) = vals[i→n(i)]
Proof step 82:
0 ≤ i2 + i ∧ i2 + i < n→i(# (mklist(initial_value(ty), i→n(i)) + vals + mklist(initial_value(ty), i→n(i0)))), 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 ⊦ vals = [], vals[i→n(i2)] = (mklist(initial_value(ty), i→n(i)) + vals + mklist(initial_value(ty), i→n(i0)))[i→n(i2 + i)]

Rule argument

[crewrite-arg: add-at-ok , F , [i, st, vals, ty, r] → [i2 + i, st, mklist(initial_value(ty), i→n(i)) + vals + mklist(initial_value(ty), i→n(i0)), ty, r] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ 0 ≤ i ∧ 0 ≤ j → ¬ i + j < 0], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ # (vals + vals0) = # vals + # vals0], [CSIMPSEQ : ⊦ # mklist(val, n) = n], [CSIMPSEQ : ⊦ (vals + vals0) + vals1 = vals + vals0 + vals1], [CSIMPSEQ : ⊦ n→i(m + n) = n→i(m) + n→i(n)], [CSIMPSEQ : ⊦ 0 ≤ i → n→i(i→n(i)) = i], [CSIMPSEQ : ⊦ 0 < i → n→i(i→n(i)) = i], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ i + j < i + i0 ↔ j < i0], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPFORWARD : ⊦ i ≤ j ∧ j < j0 → i < j0], [CSIMPSEQ : ⊦ i + j < j ↔ i < 0], [CSIMPSEQ : ⊦ i < j → ¬ j < i])], [EXTRATERMS : (i2 + i, st, mklist(initial_value(ty), i→n(i)) + vals + mklist(initial_value(ty), i→n(i0)), ty, r)]]