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Proof step 8 from proof lebs-size-mappedfull (previous step)

n + m0 + 1 < # avol, ∀ n0. n ≤ n0 ∧ ¬ n + m0 < n0 ∧ n0 < # avol → avol[n0].mapped? ∧ # avol[n0].data = LEB_SIZE ⊦ # lebs(avol, n, m0 + 1) = LEB_SIZE * m0 + LEB_SIZE, n + m0 < # avol ∧ (n ≤ n0 ∧ n0 < n + m0 ∧ n0 < # avol → avol[n0].mapped? ∧ # avol[n0].data = LEB_SIZE)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
n + m0 < # avol, n0 < n + m0, n + m0 + 1 < # avol, n0 + 1 < # avol, n0 < # avol, n < # avol, n ≤ n0, ∀ n0. n ≤ n0 ∧ ¬ n + m0 < n0 ∧ n0 < # avol → avol[n0].mapped? ∧ # avol[n0].data = LEB_SIZE ⊦ # lebs(avol, n, m0) + # (avol[n + m0].mapped? ⊃ avol[n + m0].data + mkempbuf(LEB_SIZE - # avol[n + m0].data);mkempbuf(LEB_SIZE)) = LEB_SIZE * m0 + LEB_SIZE, m0 = 0, avol[n0].mapped? ∧ # avol[n0].data = LEB_SIZE

Rule argument

Additional information

Used simplifier rules: lebs-rec: ⊦ n + m < # avol → lebs(avol, n, m + 1) = lebs(avol, n, m) + (avol[n + m].mapped? ⊃ avol[n + m].data + mkempbuf(LEB_SIZE - # avol[n + m].data) ;mkempbuf(LEB_SIZE) );% ⊦ m < m + n ↔ n ≠ 0; (s)% ⊦ m +1 = m + 1; (s)% ⊦ m < n → n ≠ 0; (s)%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat%transitivity: ⊦ n < n0 ∧ n0 < n1 → n < n1; (forward) from specification oelem[nat-set]%lf: ⊦ m < n ∧ n < n0 → m +1 < n0; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ #(buf + buf0) = # buf + # buf0; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ ¬ m < n → ¬ m + m0 < n; (s)