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Proof step 6 from proof subarray-add-eq-mkempbuf (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ buf = buf0 ↔ # buf = # buf0 ∧ (∀ n. n < # buf → buf[n] = buf0[n])
Proof step 8:
m + n0 + n1 ≤ # buf, ∀ n. n < n0 + n1 → buf[m + n] = empty ⊦ # subarray(buf, m, n0) = # mkempbuf(n0) ∧ (∀ n. n < # subarray(buf, m, n0) → subarray(buf, m, n0)[n] = mkempbuf(n0)[n])

Rule argument

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

Additional information

Used terms: mkempbuf(n0), subarray(buf, m, n0)