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Proof step 25 from proof prepost-read-lebs (previous step)

# buf = (n2 + n1) * LEB_SIZE, avol[n3 + n1] = mapped(buf0), subarray(buf, 0, n1 * LEB_SIZE) = lebs(avol, n3, n1), n3 + n1 < # avol, ebm-vol-inv(avol), mapped-full?(avol, n3, n2 + n1), 1 ≤ n2, # buf0 ≤ LEB_SIZE, n3 + n2 + n1 ≤ # avol, n1 * LEB_SIZE + LEB_SIZE ≤ # buf, LEB_SIZE ≤ # buf0 + (LEB_SIZE - # buf0) ⊦ lebs(avol, n3, n1) + buf0 + mkempbuf(LEB_SIZE - # buf0) = lebs(avol, n3, n1 + 1), n2 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 26:
⊦ 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))

Rule argument

spec: persistence-io-inv 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] → [n1, n3, avol] flags: <all paths>

Additional information

Used simplifier rules: ⊦ buf + buf0 = buf + buf1 ↔ buf0 = buf1; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ mapped(buf).mapped?; (s)% ⊦ mapped(buf).data = buf; (s)%# buf = n ⊦ subarray(buf, 0, n) = buf; (s) Used terms: n1, n3, avol