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Proof step 159 from proof putarray-addarray-override (previous step)

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]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 119:
⊦ i ≥ 0 → (((* i)) + n→i(n) ≤ n→i(m) ↔ i→n(i) + n ≤ m)
Proof step 158:
i ≥ 0, i→n(i0) = n + i→n(i), i < n→i(# vals0), 0 ≤ i, i→n(i) + # vals ≤ # 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

[speclemmaarg: ,i ≥ 0 → (((* i)) + n→i(n) ≤ n→i(m) ↔ i→n(i) + n ≤ m) ,[m, n, i] → [# vals0, # vals, i] ,F ,intnat , ,le-int-le-nat ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i ≥ j ↔ ¬ i < j], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)])], [EXTRATERMS : (# vals0, # vals, i)]]