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Proof step 6 from proof subbarray-alignup-datasize-empty (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ datasize(buf, m) ≤ n ∧ n < m ∧ m ≤ # buf → buf[n] = empty

Rule argument

spec: datasize name: datasize-at-h seq: ⊦ datasize(buf, m) ≤ n ∧ n < m ∧ m ≤ # buf → buf[n] = empty subst: [m, n, buf] → [n0, align↑(datasize(buf, n0), EB_PAGE_SIZE) + n, buf] flags: <all paths>

Additional information

Used simplifier rules: a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m = m0 + n0 ∧ n < n0 → m0 + n < m; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ EB_PAGE_SIZE ≠ 0; (s)% ⊦ m ≤ m; (s)%m ≠ 0, n1 ≤ n0 ⊦ ¬ align↑(n0, m) + n2 < n1; (s) Used terms: n0, align↑(datasize(buf, n0), EB_PAGE_SIZE) + n, buf