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Proof step 4 from proof lebs-idexpt-below (previous step)

# avol1 = # avol0, n < m0, id○(avol1, avol0, n), m0 + m +1 ≤ # avol0, ∀ avol1, avol0, n, m0. # avol1 = # avol0 ∧ n < m0 ∧ id○(avol1, avol0, n) ∧ m0 + m ≤ # avol0 → lebs(avol1, m0, m) = lebs(avol0, m0, m) ⊦ lebs(avol1, m0, m +1) = lebs(avol0, m0, m +1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
# avol1 = # avol0, m0 + m < # avol0, n < m0, id○(avol1, avol0, n), ∀ avol1, avol0, n, m0. # avol1 = # avol0 ∧ n < m0 ∧ id○(avol1, avol0, n) ∧ m0 + m ≤ # avol0 → lebs(avol1, m0, m) = lebs(avol0, m0, m) ⊦ lebs(avol1, m0, m) + (avol1[m0 + m].mapped? ⊃ avol1[m0 + m].data + mkempbuf(LEB_SIZE - # avol1[m0 + m].data);mkempbuf(LEB_SIZE)) = lebs(avol0, m0, m) + (avol0[m0 + m].mapped? ⊃ avol0[m0 + m].data + mkempbuf(LEB_SIZE - # avol0[m0 + m].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)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%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)