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Proof step 17 from proof ebm-cons-above-fillcount (previous step)

# buf = LEB_SIZE, LEB_SIZE = n0 + m0, avols[v][m] = mapped(buf, m0), m < # avols[v], m1 < n0, is-aligned(m0, EB_PAGE_SIZE), v ∈ avols, m0 ≤ LEB_SIZE, m0 + n0 ≤ # buf, 0 + n0 ≤ # emptyleb, ∀ n. n < n0 → buf[m0 + n] = (emptyleb)[0 + n] ⊦ buf[m1 + m0] = empty

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 18:
# buf = LEB_SIZE, LEB_SIZE = n0 + m0, avols[v][m] = mapped(buf, m0), m1 < n0, m < # avols[v], m1 < LEB_SIZE, is-aligned(m0, EB_PAGE_SIZE), v ∈ avols, m0 ≤ LEB_SIZE, n0 ≤ LEB_SIZE, ∀ n. n < n0 → buf[m0 + n] = empty ⊦ buf[m1 + m0] = empty

Rule argument

Additional information

Used simplifier rules: lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic% ⊦ m ≤ m; (s)%n < # emptyleb ⊦ (emptyleb)[n] = empty; (s)% ⊦ m < n → (n ≤ m ↔ false); (s)%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat%let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ # emptyleb = LEB_SIZE; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ n + 0 = n; (s)