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Proof step 189 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)) ⊦ (putArray(vals, r0, i, addarray(r0, ty, vals0, st))[r0 -- i0 ']) = (firstn(i→n(i), vals0) + vals + restn(i→n(i) + # vals, vals0))[i→n(i0)]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 110:
⊦ r ≠ r0 → (putArray(vals, r, j, st)[r0 -- sk]) = st[r0 -- sk]
Proof step 188:
¬ r0 ≠ r0, 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)) ⊦ (putArray(vals, r0, i, addarray(r0, ty, vals0, st))[r0 -- i0 ']) = (firstn(i→n(i), vals0) + vals + restn(i→n(i) + # vals, vals0))[i→n(i0)]

Rule argument

[speclemmaarg: ,r ≠ r0 → (putArray(vals, r, j, st)[r0 -- sk]) = st[r0 -- sk] ,[sk, r0, st, j, r, vals] → [i0 ', r0, addarray(r0, ty, vals0, st), i, r0, vals] ,F ,storearrays , ,putar-atref ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (i0 ', r0, addarray(r0, ty, vals0, st), i, r0, vals)]]