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Proof step 160 from proof putarray-addarray-override (previous step)

i→n(i) + # vals ≤ # vals0, i→n(i0) = n + i→n(i), 0 < i + n→i(# vals) + n→i(# vals0 - i→n(i) + # vals), 0 ≤ i0, i0 < i + n→i(# vals) + n→i(# vals0 - i→n(i) + # vals), i + n→i(# vals) ≤ n→i(# vals0), 0 ≤ i, 0 < n→i(# vals) + n→i(# vals0 - i→n(i) + # vals), i ≤ i0 ⊦ (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 159:
i→n(i0) = n + i→n(i), i < n→i(# vals0), 0 ≤ i, i + n→i(# vals) ≤ n→i(# vals0), i0 < n→i(# vals0), 0 ≤ i0, i→n(i) + # vals ≤ # vals0, i ≤ i0 ⊦ vals0 = [], (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 : ([CSIMPFORWARD : ⊦ i ≤ j ∧ j < j0 → i < j0], [CSIMPFORWARD : ⊦ i < j ∧ 0 ≤ i → 0 < j], [CSIMPSEQ : ⊦ i + 0 = i], [CSIMPSEQ : ⊦ i < j - i0 ↔ i + i0 < j], [CSIMPSEQ : ⊦ i + j - i0 + j = i - i0], [CSIMPSEQ : ⊦ i + (j - i0) = i + j - i0], [CSIMPSEQ : ⊦ # vals = 0 ↔ vals = []], [CSIMPSEQ : ⊦ 0 < n ↔ n ≠ 0], [CSIMPSEQ : 0 ≤ i ⊦ ((* i)) < n→i(n) ↔ i→n(i) < n], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + (j - i) = j], [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)], [CSIMPSEQ : ⊦ n ≤ m → n→i(m - n) = n→i(m) - n→i(n)])]]