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Proof step 116 from proof putarray-addarray-override (previous step)

0 ≤ i0, i0 = n→i(n + i→n(i)), # vals0 < i→n(i) + # vals, i ≤ i0, 0 < n→i(# vals) + n→i(# restn(i→n(i) + # vals, vals0)), 0 ≤ i, i + n→i(# vals) ≤ n→i(# vals0), i0 < i + n→i(# vals) + n→i(# restn(i→n(i) + # vals, vals0)), 0 ≤ i0, 0 < i + n→i(# vals) + n→i(# restn(i→n(i) + # vals, vals0)) ⊦ (putArray(vals, r0, i, addarray(r0, ty, vals0, st))[r0 -- i0 ']) = (vals + restn(i→n(i) + # vals, vals0))[n]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 115:
0 < i + n→i(# vals) + n→i(# restn(i→n(i) + # vals, vals0)), # vals0 < i→n(i) + # vals, 0 < n→i(# vals) + n→i(# restn(i→n(i) + # vals, vals0)), 0 ≤ i, i + n→i(# vals) ≤ n→i(# vals0), n→i(n) < n→i(# vals) + n→i(# restn(i→n(i) + # vals, vals0)), 0 ≤ n→i(n) + i ⊦ (putArray(vals, r0, i, addarray(r0, ty, vals0, st))[r0 -- (n→i(n) + i) ']) = (vals + restn(i→n(i) + # vals, vals0))[n]

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPSEQ : ⊦ i + j < i + i0 ↔ j < i0], [CSIMPSEQ : ⊦ 0 ≤ n→i(n)], [CSIMPSEQ : ⊦ i ≤ i + j ↔ 0 ≤ j], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ 0 ≤ i → n→i(i→n(i)) = i], [CSIMPSEQ : ⊦ n→i(m + n) = n→i(m) + n→i(n)])]]