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Proof step 11 from proof lebs-crash (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
n < # avol0, n0 < n + m0, n + m0 < # avol1, n + m0 < # avol0, n0 + 1 < # avol1, n0 + 1 < # avol0, n0 < # avol1, n0 < # avol0, n < # avol1, n ≤ n0, avol0 ⊆ avol1, ∀ n0. n ≤ n0 ∧ ¬ n + m0 < n0 ∧ n0 < # avol0 → avol0[n0].mapped? ∧ # avol0[n0].data = LEB_SIZE ⊦ lebs(avol1, n, m0) + (avol1[n + m0].mapped? ⊃ avol1[n + m0].data + mkempbuf(LEB_SIZE - # avol1[n + m0].data);mkempbuf(LEB_SIZE)) = lebs(avol0, n, m0) + (avol0[n + m0].mapped? ⊃ avol0[n + m0].data + mkempbuf(LEB_SIZE - # avol0[n + m0].data);mkempbuf(LEB_SIZE)), m0 = 0, avol0[n0].mapped? ∧ # avol0[n0].data = LEB_SIZE

Rule argument

Additional information

Used simplifier rules: c: ⊦ m + n = n + m; from specification nat-basic%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%transitivity: ⊦ n < n0 ∧ n0 < n1 → n < n1; (forward) from specification oelem[nat-set]%lf: ⊦ m < n ∧ n < n0 → m +1 < n0; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic