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Proof step 11 from proof tolist-at (previous step)

inv(buf), m ≤ n0, m < n0 → (tolist(buf, n0)[m]) = (buf .data)[(i→n(buf .first) + m) % i→n(buf .size)] ⊦ (tolist(buf, n0) + (buf .data)[(i→n(buf .first) + n0) % i→n(buf .size)] ')[m] = (buf .data)[(i→n(buf .first) + m) % i→n(buf .size)]

User applied rule case distinction

And obtained the following new goals

Proof step 6:
inv(buf), m ≤ n0 ⊦ m < n0, (tolist(buf, n0) + (buf .data)[(i→n(buf .first) + n0) % i→n(buf .size)] ')[m] = (buf .data)[(i→n(buf .first) + m) % i→n(buf .size)]
Proof step 10:
(tolist(buf, n0)[m]) = (buf .data)[(i→n(buf .first) + m) % i→n(buf .size)], inv(buf), m ≤ n0 ⊦ (tolist(buf, n0) + (buf .data)[(i→n(buf .first) + n0) % i→n(buf .size)] ')[m] = (buf .data)[(i→n(buf .first) + m) % i→n(buf .size)]

Rule argument

[CASEDARG : pos: left 3, ()]

Additional information

[[CONCRETESIMPRULES : ()]]