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Proof step 137 from proof putarray-addarray-override (previous step)

0 ≤ i, i→n(i) < # vals0, i→n(i) + # vals ≤ # vals0, i→n(i) + n0 + # vals < # vals0, 0 ≤ (n→i(n0) + n→i(# vals)) + i, (i→n(i) + # vals) + n0 < # vals0, 0 ≤ i + n→i(# vals) ⊦ vals0 = [], vals0[i→n(i) + n0 + # vals] = (restn(i→n(i) + # vals, vals0)[n0])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 132:
⊦ m + n = n + m
Proof step 136:
0 ≤ i, i→n(i) < # vals0, # vals + i→n(i) ≤ # vals0, i→n(i) + n0 + # vals < # vals0, 0 ≤ (n→i(n0) + n→i(# vals)) + i, (# vals + i→n(i)) + n0 < # vals0, 0 ≤ i + n→i(# vals) ⊦ vals0 = [], vals0[i→n(i) + n0 + # vals] = (restn(# vals + i→n(i), vals0)[n0])

Rule argument

[speclemmaarg: ,m + n = n + m ,[n, m] → [# vals, i→n(i)] ,F ,nat-basic2 , ,c ]

Additional information

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