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Proof step 32 from proof datasize-further (previous step)

n + 1 = datasize(buf, n1), datasize(buf, n1) < n1, n < n1, n < # buf, n0 < n1, n < n0, datasize(buf, n1) ≤ # buf, datasize(buf, n1) ≤ n0, n ≤ n1 ∧ n ≤ # buf → (datasize(buf, n) = datasize(buf, n1) ↔ (∀ n2. n ≤ n2 ∧ n2 < n1 → buf[n2] = empty)) ⊦ buf[n] = empty, buf[n0] = empty

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 33:
n + 1 = datasize(buf, n1), datasize(buf, n) = datasize(buf, n1) ↔ (∀ n2. n ≤ n2 ∧ n2 < n1 → buf[n2] = empty), n < n0, n0 < n1, n < # buf, n < n1, datasize(buf, n1) < n1, datasize(buf, n1) ≤ n0, datasize(buf, n1) ≤ # buf ⊦ buf[n0] = empty, buf[n] = empty

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → m ≤ n; (s)