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Proof step 9 from proof mapped-full-last (previous step)

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

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 10:
# 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

Rule argument

fma: n0 = m + n

Additional information

Used simplifier rules: ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)% ⊦ m ≤ m; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m ≤ m + n; (s)% ⊦ m < # avol → avol[m, aleb][m] = aleb; (s)% ⊦ mapped(buf).mapped?; (s)% ⊦ mapped(buf).data = buf; (s) Used formulas: n0 = m + n