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Proof step 8 from proof mapped-full-last (previous step)

# buf = LEB_SIZE, m + n < # avol, ∀ n0. n ≤ n0 ∧ n0 < n + m ∧ n0 < # avol → avol[n0].mapped? ∧ # avol[n0].data = LEB_SIZE ⊦ ∀ n0. n ≤ n0 ∧ ¬ n + m < n0 ∧ n0 < # avol → 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 9:
# 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

Rule argument

Additional information

Used simplifier rules: a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m ≤ m + n; (s)%let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m < n ↔ ¬ n ≤ m; (ss)