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Proof step 161 from proof putarray-addarray-override (previous step)

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]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 112:
n ≤ # vals ⊦ # restn(n, vals) = # vals - n
Proof step 118:
¬ i→n(i) + # vals ≤ # vals0, 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]
Proof step 160:
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]

Rule argument

[speclemmaarg: n ≤ # vals ,# restn(n, vals) = # vals - n ,[vals, n] → [vals0, i→n(i) + # vals] ,F ,list-del ,javavalues ,rest-len ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (vals0, i→n(i) + # vals)]]