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Proof step 185 from proof putarray-addarray-override (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 165:
⊦ n < m ∧ m ≤ # vals → (firstn(m, vals)[n]) = vals[n]
Proof step 168:
¬ (i→n(i0) < i→n(i) ∧ i→n(i) ≤ # vals0), 0 ≤ i, i + n→i(# vals) ≤ n→i(# vals0), i0 < i + n→i(# vals) + n→i(# restn(i→n(i) + # vals, vals0)), 0 ≤ i0, 0 < i + n→i(# vals) + n→i(# restn(i→n(i) + # vals, vals0)), i0 < i, 0 < i ⊦ (putArray(vals, r0, i, addarray(r0, ty, vals0, st))[r0 -- i0 ']) = (firstn(i→n(i), vals0)[i→n(i0)])
Proof step 184:
i→n(i0) < i→n(i) ∧ i→n(i) ≤ # vals0, 0 ≤ i, i + n→i(# vals) ≤ n→i(# vals0), i0 < i + n→i(# vals) + n→i(# restn(i→n(i) + # vals, vals0)), 0 ≤ i0, 0 < i + n→i(# vals) + n→i(# restn(i→n(i) + # vals, vals0)), i0 < i, 0 < i ⊦ (putArray(vals, r0, i, addarray(r0, ty, vals0, st))[r0 -- i0 ']) = vals0[i→n(i0)]

Rule argument

[speclemmaarg: ,n < m ∧ m ≤ # vals → (firstn(m, vals)[n]) = vals[n] ,[n, vals, m] → [i→n(i0), vals0, i→n(i)] ,F ,list-del ,javavalues ,get-firstn ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (i→n(i0), vals0, i→n(i))]]