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Proof step 10 from proof mapped-full-last (previous step)

# buf = LEB_SIZE, n0 < # avol, m + n < # avol, n < # avol, n ≤ n0, n0 ≤ n + m, ∀ n0. n ≤ n0 ∧ n0 < n + m ∧ n0 < # avol → avol[n0].mapped? ∧ # avol[n0].data = LEB_SIZE ⊦ n0 = m + n, avol[m + n, mapped(buf)][n0].mapped? ∧ # avol[m + n, mapped(buf)][n0].data = LEB_SIZE

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 11:
# buf = LEB_SIZE, n0 < n + m, n0 < # avol, m + n < # avol, n < # avol, n0 + 1 < # avol, n ≤ n0, ∀ n0. n ≤ n0 ∧ n0 < n + m ∧ n0 < # avol → avol[n0].mapped? ∧ # avol[n0].data = LEB_SIZE ⊦ m = 0, n0 = m + n, avol[n0].mapped? ∧ # avol[n0].data = LEB_SIZE

Rule argument

Additional information

Used simplifier rules: a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ 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%lf: ⊦ m < n ∧ n < n0 → m +1 < n0; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ n < m → avol[m, aleb][n] = avol[n]; (s)% ⊦ m ≠ n → (m ≤ n ↔ m < n); (s)%c: ⊦ m + n = n + m; from specification nat-basic