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Proof step 157 from proof putarray-addarray-override (previous step)

i→n(i0) = n + i→n(i), i < n→i(# vals0), 0 ≤ i, 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 120:
0 ≤ i ⊦ ((* i)) < n→i(n) ↔ i→n(i) < n
Proof step 156:
0 ≤ i, i→n(i0) = n + i→n(i), i→n(i) < # vals0, 0 ≤ i, 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: 0 ≤ i ,((* i)) < n→i(n) ↔ i→n(i) < n ,[n, i] → [# vals0, i] ,F ,intnat , ,num-n2i-ls-02 ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (# vals0, i)]]