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Proof step 4 from proof lebs-crash (previous step)

n + m0 +1 ≤ # avol0, avol0 ⊆ avol1, ∀ n0. n ≤ n0 ∧ n0 < n + m0 +1 ∧ n0 < # avol0 → avol0[n0].mapped? ∧ # avol0[n0].data = LEB_SIZE, ∀ n, avol0, avol1. n + m0 ≤ # avol0 ∧ avol0 ⊆ avol1 ∧ (∀ n0. n ≤ n0 ∧ n0 < n + m0 ∧ n0 < # avol0 → avol0[n0].mapped? ∧ # avol0[n0].data = LEB_SIZE) → lebs(avol1, n, m0) = lebs(avol0, n, m0) ⊦ lebs(avol1, n, m0 +1) = lebs(avol0, n, m0 +1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
n + m0 < # avol0, avol0 ⊆ avol1, ∀ n0. n ≤ n0 ∧ ¬ n + m0 < n0 ∧ n0 < # avol0 → avol0[n0].mapped? ∧ # avol0[n0].data = LEB_SIZE, ∀ n, avol0, avol1. n + m0 ≤ # avol0 ∧ avol0 ⊆ avol1 ∧ (∀ n0. n ≤ n0 ∧ n0 < n + m0 ∧ n0 < # avol0 → avol0[n0].mapped? ∧ # avol0[n0].data = LEB_SIZE) → lebs(avol1, n, m0) = lebs(avol0, n, m0) ⊦ lebs(avol1, n, m0 + 1) = lebs(avol0, n, m0) + (avol0[n + m0].mapped? ⊃ avol0[n + m0].data + mkempbuf(LEB_SIZE - # avol0[n + m0].data);mkempbuf(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 < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m < n + 1 ↔ ¬ n < m; (s)%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m + 1 ≤ n ↔ m < n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m +1 = m + 1; (s)