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Proof step 216 from proof putarray-addarray-override (previous step)

0 ≤ i, i + n→i(# vals) ≤ n→i(# vals0) ⊦ (rk ∈ putArray(vals, r, i, addarray(r, ty, vals0, st)) ↔ rk ∈ addarray(r, ty, firstn(i→n(i), vals0) + vals + restn(i→n(i) + # vals, vals0), st)) ∧ (putArray(vals, r, i, addarray(r, ty, vals0, st))[rk]) = (addarray(r, ty, firstn(i→n(i), vals0) + vals + restn(i→n(i) + # vals, vals0), st)[rk])

User applied rule structural induction

And obtained the following new goals

Proof step 215:
0 ≤ i, i + n→i(# vals) ≤ n→i(# vals0) ⊦ ( r0 -- sk ∈ 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)) ∧ (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])

Rule argument

[VARWITHVARSEQSARG : rk, ()]

Additional information

[[CONCRETESIMPRULES : ([CSIMPGEN : refkey generated by --;])]]