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

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ 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 6:
n0 < n, n + m0 < # avol, n + m0 < # avol[n0, aleb], ∀ n0, n, avol, aleb. n0 < n ∧ n + m0 ≤ # avol → lebs(avol[n0, aleb], n, m0) = lebs(avol, n, m0) ⊦ lebs(avol[n0, aleb], n, m0) + (avol[n0, aleb][n + m0].mapped? ⊃ avol[n0, aleb][n + m0].data + mkempbuf(LEB_SIZE - # avol[n0, aleb][n + m0].data);mkempbuf(LEB_SIZE)) = lebs(avol, n, m0) + (avol[n + m0].mapped? ⊃ avol[n + m0].data + mkempbuf(LEB_SIZE - # avol[n + m0].data);mkempbuf(LEB_SIZE))

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] → [m0, n, avol[n0, aleb]] flags: <all paths>

Additional information

Used simplifier rules: ⊦ # avol[n, aleb] = # avol; (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m < n → (n ≤ m ↔ false); (s) Used terms: m0, n, avol[n0, aleb]