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Proof step 10 from proof ls-datasize-zero (previous step)

# buf = n1 + n, n0 < n1 + n, ∀ n0. n0 < n → buf[n0] = empty ⊦ buf[n0] = (mkempbuf(n) + subarray(buf, n, n1))[n0]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ n < # buf → (buf + buf0)[n] = buf[n]
Proof step 12:
# buf = n1 + n, n0 < n1 + n, ∀ n0. n0 < n → buf[n0] = empty ⊦ buf[n0] = (mkempbuf(n) + subarray(buf, n, n1))[n0], n0 < # mkempbuf(n)
Proof step 17:
# buf = n1 + n, n0 < n1 + n, n0 < # mkempbuf(n), ∀ n0. n0 < n → buf[n0] = empty ⊦ buf[n0] = mkempbuf(n)[n0]

Rule argument

spec: array-splice, inst: buffer name: append-at1 seq: ⊦ n < # buf → (buf + buf0)[n] = buf[n] subst: [n, buf0, buf] → [n0, subarray(buf, n, n1), mkempbuf(n)] flags: <all paths>

Additional information

Used terms: n0, subarray(buf, n, n1), mkempbuf(n)