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Proof step 88 from proof putarray-addarray-override (previous step)

# vals0 < i→n(i) + # vals, 0 ≤ i, i + n→i(# vals) ≤ n→i(# vals0), i + n→i(# vals) + n→i(# restn(i→n(i) + # vals, vals0)) ≤ i0, n→i(# vals) + i ≤ i0, # vals0 ≤ i→n(i0), 0 ≤ i0, i0 < n→i(# vals0), i + n→i(# vals) + n→i(# restn(i→n(i) + # vals, vals0)) < n→i(# vals0), n→i(# vals) + i < n→i(# vals0) ⊦ vals0 = [], vals0[i→n(i0)] = st[r0 -- i0 ']

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 81:
n ≤ # vals ⊦ # restn(n, vals) = # vals - n
Proof step 87:
¬ i→n(i) + # vals ≤ # vals0, # vals0 < i→n(i) + # vals, 0 ≤ i, i + n→i(# vals) ≤ n→i(# vals0), i + n→i(# vals) + n→i(# restn(i→n(i) + # vals, vals0)) ≤ i0, n→i(# vals) + i ≤ i0, # vals0 ≤ i→n(i0), 0 ≤ i0, i0 < n→i(# vals0), i + n→i(# vals) + n→i(# restn(i→n(i) + # vals, vals0)) < n→i(# vals0), n→i(# vals) + i < n→i(# vals0) ⊦ vals0 = [], vals0[i→n(i0)] = st[r0 -- i0 ']

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 : ([CSIMPSEQ : ⊦ m < n → (n ≤ m ↔ false)])], [EXTRATERMS : (vals0, i→n(i) + # vals)]]