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Proof step 34 from proof prepost-read-lebs (previous step)

# buf = (n2 + n1) * LEB_SIZE, # buf = n0 + n1 * LEB_SIZE + LEB_SIZE, avol[n3 + n1] = mapped(buf0), subarray(buf, 0, n1 * LEB_SIZE) = lebs(avol, n3, n1), n3 + n1 < # avol, ebm-vol-inv(avol), mapped-full?(avol, n3, n2 + n1), n3 + n2 + n1 ≤ # avol, n1 * LEB_SIZE + LEB_SIZE ≤ # buf, ⌊err0⌋ ⊦ n2 = 0, ∃ buf1. # buf1 = # buf ∧ range=(buf, 0, buf1, 0, n1 * LEB_SIZE) ∧ range=(buf, n1 * LEB_SIZE + LEB_SIZE, buf1, n1 * LEB_SIZE + LEB_SIZE, n0)

User applied rule exists right

And closed the goal!

Rule argument

pos: right 2 terms: buf abort: F discard: T computed: F

Additional information

Used simplifier rules: ⊦ range=(buf, n, buf, n, m) ↔ n + m ≤ # buf; (s)% ⊦ n + 0 = n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m ≤ m; (s)% ⊦ m ≠ n → (m ≤ n ↔ m < n); (s)% ⊦ n ≠ n0 → (n < n0 ↔ ¬ n0 < n); (ss)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat% ⊦ m0 * m = 0 ↔ m0 = 0 ∨ m = 0; (ws)% ⊦ LEB_SIZE ≠ 0; (s)%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult% ⊦ m + m0 < n → ¬ n + n0 < m; (s)%# buf = n ⊦ subarray(buf, 0, n) = buf; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m < n → (n ≤ m ↔ false); (s)%n + m < # avol ⊦ ebm-vol-inv(avol) → # lebs(avol, n, m) = m * LEB_SIZE; (s)% ⊦ m = m + n ↔ n = 0; (s)% ⊦ m + n = 0 ↔ m = 0 ∧ n = 0; (ws) Used terms: buf