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Proof step 151 from proof putarray-addarray-override (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 123:
⊦ i ≥ 0 → (((* i)) + n→i(n) < n→i(m) ↔ i→n(i) + n < m)
Proof step 150:
i ≥ 0, 0 ≤ i, i→n(i) < # vals0, i→n(i) + # vals ≤ # vals0, i→n(i) + n < # vals0, 0 ≤ n→i(n) + i ⊦ vals0 = [], (putArray(vals, r0, i, addarray(r0, ty, vals0, st))[r0 -- (n→i(n) + i) ']) = (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, i, n] → [# vals0, i, n] ,F ,intnat , ,ls-int-ls-nat ]

Additional information

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