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Proof step 1 from proof subarray-append-mkempbuf-from (conclusion)

n2 ≤ n1 + # buf ⊦ subarray(mkempbuf(n0 + n1) + buf, n0, n2) = subarray(mkempbuf(n1) + buf, 0, n2)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ buf = buf0 ↔ # buf = # buf0 ∧ (∀ n. n < # buf → buf[n] = buf0[n])
Proof step 3:
n2 ≤ n1 + # buf ⊦ # subarray(mkempbuf(n0 + n1) + buf, n0, n2) = # subarray(mkempbuf(n1) + buf, 0, n2) ∧ (∀ n. n < # subarray(mkempbuf(n0 + n1) + buf, n0, n2) → subarray(mkempbuf(n0 + n1) + buf, n0, n2)[n] = subarray(mkempbuf(n1) + buf, 0, n2)[n])

Rule argument

spec: array, inst: buffer name: Extension seq: ⊦ buf = buf0 ↔ # buf = # buf0 ∧ (∀ n. n < # buf → buf[n] = buf0[n]) subst: [buf0, buf] → [subarray(mkempbuf(n1) + buf, 0, n2), subarray(mkempbuf(n0 + n1) + buf, n0, n2)] flags: <all paths>

Additional information

Used terms: subarray(mkempbuf(n1) + buf, 0, n2), subarray(mkempbuf(n0 + n1) + buf, n0, n2)