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Proof step 39 from proof prepost-read-lebs (previous step)

# buf = (n2 + n1) * LEB_SIZE, buf0 = buf, m = 0, m0 = n3 + n1, n = LEB_SIZE, n0 = n1 * LEB_SIZE, subarray(buf, 0, n1 * LEB_SIZE) = lebs(avol, n3, n1), ebm-vol-inv(avol), mapped-full?(avol, n3, n2 + n1), n3 + n2 + n1 ≤ # avol, m0 < # avol → m0 < # avol ⊦ n2 = 0, m0 < # avol ∧ avol[m0].mapped? ∧ n0 + n ≤ # buf0 ∧ m + n ≤ LEB_SIZE

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 40:
# buf = (n2 + n1) * LEB_SIZE, avol[n3 + n1] = unmapped, subarray(buf, 0, n1 * LEB_SIZE) = lebs(avol, n3, n1), n3 + n1 < # avol, ebm-vol-inv(avol), mapped-full?(avol, n3, n2 + n1), n1 * LEB_SIZE + LEB_SIZE ≤ # buf, n3 + n2 + n1 ≤ # avol ⊦ n2 = 0

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)% ⊦ aleb.mapped? ↔ aleb ≠ unmapped; (ss)%mult-c: ⊦ m * n = n * m; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult% ⊦ m < 1 ↔ m = 0; (s)% ⊦ m + n < m + n0 ↔ n < n0; (s)% ⊦ m * n < m1 * n + n ↔ m < m1 + 1 ∧ n ≠ 0; (s)% ⊦ LEB_SIZE + n ≠ 0; (s)%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ m + m0 ≤ m ↔ m0 = 0; (s)% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)%let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m ≤ m; (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)