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Proof step 4 from proof lebs-size-mappedfull (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
n + m0 + 1 < # avol, ∀ n, avol. n + m0 < # avol ∧ (∀ n0. n ≤ n0 ∧ n0 < n + m0 ∧ n0 < # avol → avol[n0].mapped? ∧ # avol[n0].data = LEB_SIZE) → # lebs(avol, n, m0) = m0 * LEB_SIZE, ∀ 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

Rule argument

Additional information

Used simplifier rules: ⊦ m < n + 1 ↔ ¬ n < m; (s)%mult-c: ⊦ m * n = n * m; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m * (n + 1) = m * n + m; (s)% ⊦ m +1 = m + 1; (s)