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Proof step 5 from proof subbarray-alignup-datasize-empty (previous step)

n0 = n1 + align↑(datasize(buf, n0), EB_PAGE_SIZE), n0 ≤ # buf ⊦ # subarray(buf, align↑(datasize(buf, n0), EB_PAGE_SIZE), n1) = # mkempbuf(n1) ∧ (∀ n. n < # subarray(buf, align↑(datasize(buf, n0), EB_PAGE_SIZE), n1) → subarray(buf, align↑(datasize(buf, n0), EB_PAGE_SIZE), n1)[n] = mkempbuf(n1)[n])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
n0 = n1 + align↑(datasize(buf, n0), EB_PAGE_SIZE), n < n1, n0 ≤ # buf ⊦ buf[align↑(datasize(buf, n0), EB_PAGE_SIZE) + n] = empty

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m < n → mkempbuf(n)[m] = empty; (s)% ⊦ n0 < n → subarray(buf, m, n)[n0] = buf[m + n0]; (s)% ⊦ # mkempbuf(n) = n; (s)% ⊦ # subarray(buf, m, n) = n; (s)