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Proof step 5 from proof lebs-range-eq (previous step)

n0 + n < m + m2, range=(avol0, m, avol1, m, m2), m ≤ n0, ∀ avol0, m, avol1, m2, n0. range=(avol0, m, avol1, m, m2) ∧ n0 + n ≤ m + m2 ∧ m ≤ n0 → lebs(avol0, n0, n) = lebs(avol1, n0, n) ⊦ lebs(avol0, n0, n + 1) = lebs(avol1, n0, n + 1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ 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))
Proof step 7:
n0 + n < m + m2, range=(avol0, m, avol1, m, m2), m ≤ n0, ∀ avol0, m, avol1, m2, n0. range=(avol0, m, avol1, m, m2) ∧ n0 + n ≤ m + m2 ∧ m ≤ n0 → lebs(avol0, n0, n) = lebs(avol1, n0, n) ⊦ lebs(avol0, n0, n + 1) = lebs(avol1, n0, n + 1), n0 + n < # avol0
Proof step 10:
n0 + n < m + m2, n0 + n < # avol0, range=(avol0, m, avol1, m, m2), m ≤ n0, ∀ avol0, m, avol1, m2, n0. range=(avol0, m, avol1, m, m2) ∧ n0 + n ≤ m + m2 ∧ m ≤ n0 → lebs(avol0, n0, n) = lebs(avol1, n0, n) ⊦ lebs(avol0, n0, n) + (avol0[n0 + n].mapped? ⊃ avol0[n0 + n].data + mkempbuf(LEB_SIZE - # avol0[n0 + n].data);mkempbuf(LEB_SIZE)) = lebs(avol1, n0, n + 1)

Rule argument

spec: <toplevel> name: lebs-rec seq: ⊦ 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) ) subst: [m, n, avol] → [n, n0, avol0] flags: <all paths>

Additional information

Used terms: n, n0, avol0