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Proof step 214 from proof putarray-addarray-override (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 64:
⊦ r ≠ r0 → (putArray(vals, r, j, st)[r0 -- sk]) = st[r0 -- sk]
Proof step 212:
¬ r ≠ r0, 0 ≤ i, i + n→i(# vals) ≤ n→i(# vals0) ⊦ (putArray(vals, r, i, addarray(r, ty, vals0, st))[r0 -- sk]) = (addarray(r, ty, firstn(i→n(i), vals0) + vals + restn(i→n(i) + # vals, vals0), st)[r0 -- sk])
Proof step 213:
⊦ r ≠ r0 → (addarray(r, ty, vals, st)[r0 -- sk]) = st[r0 -- sk]

Rule argument

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

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (sk, r0, addarray(r, ty, vals0, st), i, r, vals)]]