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Proof step 162 from proof putarray-addarray-override (previous step)

i→n(i0) = n + i→n(i) ∧ i→n(i) ≤ i→n(i0), i ≤ i0, 0 < i + n→i(# vals) + n→i(# restn(i→n(i) + # vals, vals0)), 0 ≤ i0, i0 < i + n→i(# vals) + n→i(# restn(i→n(i) + # vals, vals0)), i + n→i(# vals) ≤ n→i(# vals0), 0 ≤ i, 0 < 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 161:
i→n(i0) = n + i→n(i), 0 < i + n→i(# vals) + n→i(# restn(i→n(i) + # vals, vals0)), 0 ≤ i0, i0 < i + n→i(# vals) + n→i(# restn(i→n(i) + # vals, vals0)), i + n→i(# vals) ≤ n→i(# vals0), 0 ≤ i, 0 < n→i(# vals) + n→i(# restn(i→n(i) + # vals, vals0)), i ≤ i0 ⊦ (putArray(vals, r0, i, addarray(r0, ty, vals0, st))[r0 -- i0 ']) = (vals + restn(i→n(i) + # vals, vals0))[n]

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ 0 ≤ i → abs(i) = i], [CSIMPSEQ : ⊦ i→n(i) ≤ i→n(j) ↔ abs(i) ≤ abs(j)])]]