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Proof step 14 from proof inv-change (previous step)

LEB_SIZE = n0 + n, m < # avols[v], ebm-cons(avols), is-aligned(n, EB_PAGE_SIZE), v ∈ avols, n ≤ LEB_SIZE, n ≤ # buf, avols[v][m].mapped? → # avols[v][m].data = LEB_SIZE ∧ avols[v][m].fill ≤ LEB_SIZE ∧ is-aligned(avols[v][m].fill, EB_PAGE_SIZE) ∧ range=(avols[v][m].data, avols[v][m].fill, emptyleb, 0, LEB_SIZE - avols[v][m].fill) ⊦ n + n0 ≤ #(subarray(buf, 0, n) + mkempbuf(n0)) ∧ 0 + n0 ≤ # emptyleb ∧ (∀ n2. n2 < n0 → (subarray(buf, 0, n) + mkempbuf(n0))[n + n2] = (emptyleb)[0 + n2])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
LEB_SIZE = n0 + n, m < # avols[v], n1 < n0, n1 < LEB_SIZE, ebm-cons(avols), is-aligned(n, EB_PAGE_SIZE), v ∈ avols, n ≤ LEB_SIZE, n ≤ # buf, n0 ≤ LEB_SIZE, avols[v][m].mapped? → # avols[v][m].data = LEB_SIZE ∧ avols[v][m].fill ≤ LEB_SIZE ∧ is-aligned(avols[v][m].fill, EB_PAGE_SIZE) ∧ range=(avols[v][m].data, avols[v][m].fill, emptyleb, 0, LEB_SIZE - avols[v][m].fill) ⊦ (subarray(buf, 0, n) + mkempbuf(n0))[n + n1] = empty

Rule argument

Additional information

Used simplifier rules: ⊦ LEB_SIZE ≠ 0; (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic% ⊦ ¬ m + n < m; (s)%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic% ⊦ m ≤ n ↔ ¬ n < m; (ss)%n < # emptyleb ⊦ (emptyleb)[n] = empty; (s)% ⊦ m < n → (n ≤ m ↔ false); (s)% ⊦ m < n → n ≠ 0; (s)%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ # emptyleb = LEB_SIZE; (s)% ⊦ n + 0 = n; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m ≤ m; (s)% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ # mkempbuf(n) = n; (s)% ⊦ # subarray(buf, m, n) = n; (s)% ⊦ #(buf + buf0) = # buf + # buf0; (s)