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Proof step 145 from proof putarray-addarray-override (previous step)

0 ≤ i, i→n(i) < # vals0, i→n(i) + # vals ≤ # vals0, i→n(i) + n < # vals0, 0 ≤ n→i(n) + i, # vals ≤ n ⊦ vals0 = [], (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 126:
⊦ 0 ≤ i ∧ i < n→i(# vals) → (addarray(r, ty, vals, st)[r -- i ']) = vals[i→n(i)]
Proof step 129:
¬ (0 ≤ n→i(n) + i ∧ n→i(n) + i < n→i(# vals0)), 0 ≤ i, i→n(i) < # vals0, i→n(i) + # vals ≤ # vals0, i→n(i) + n < # vals0, 0 ≤ n→i(n) + i, # vals ≤ n ⊦ vals0 = [], (addarray(r0, ty, vals0, st)[r0 -- (n→i(n) + i) ']) = (vals + restn(i→n(i) + # vals, vals0))[n]
Proof step 144:
0 ≤ n→i(n) + i ∧ n→i(n) + i < n→i(# vals0), 0 ≤ i, i→n(i) < # vals0, i→n(i) + # vals ≤ # vals0, i→n(i) + n < # vals0, 0 ≤ n→i(n) + i, # vals ≤ n ⊦ vals0 = [], vals0[i→n(n→i(n) + i)] = (vals + restn(i→n(i) + # vals, vals0))[n]

Rule argument

[crewrite-arg: add-at-ok , F , [i, st, vals, ty, r] → [n→i(n) + i, st, vals0, ty, r0] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (n→i(n) + i, st, vals0, ty, r0)]]