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Proof step 26 from proof inv-write (previous step)

LEB_SIZE = n0 + m, LEB_SIZE = n3 + m1 + n, avols[v][m2] = mapped(buf0, m), m2 < # avols[v], ebm-cons(avols), is-aligned(n, EB_PAGE_SIZE), is-aligned(m1, EB_PAGE_SIZE), is-aligned(m, EB_PAGE_SIZE), range=(buf0, m, emptyleb, 0, n0), v ∈ avols, n + m1 ≤ LEB_SIZE, m ≤ m1, n + n2 ≤ # buf, m1 + n ≤ LEB_SIZE, n2 + n ≤ # buf, m1 ≤ LEB_SIZE, m ≤ LEB_SIZE ⊦ n = 0, (m1 + n) + n3 ≤ #(subarray(buf0, 0, m1) + subarray(buf, n2, n) + mkempbuf(n3)) ∧ 0 + n3 ≤ # emptyleb ∧ (∀ n4. n4 < n3 → (subarray(buf0, 0, m1) + subarray(buf, n2, n) + mkempbuf(n3))[(m1 + n) + n4] = (emptyleb)[0 + n4])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 27:
LEB_SIZE = n0 + m, LEB_SIZE = n3 + m1 + n, avols[v][m2] = mapped(buf0, m), m2 < # avols[v], n1 < n3, n1 < LEB_SIZE, ebm-cons(avols), is-aligned(n, EB_PAGE_SIZE), is-aligned(m1, EB_PAGE_SIZE), is-aligned(m, EB_PAGE_SIZE), range=(buf0, m, emptyleb, 0, n0), v ∈ avols, n + m1 ≤ LEB_SIZE, m ≤ m1, n + n2 ≤ # buf, m1 + n ≤ LEB_SIZE, n2 + n ≤ # buf, m1 ≤ LEB_SIZE, m ≤ LEB_SIZE, n3 ≤ LEB_SIZE ⊦ (subarray(buf0, 0, m1) + subarray(buf, n2, n) + mkempbuf(n3))[(m1 + n) + n1] = empty, n = 0

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)