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Proof step 3 from proof subarray-add-eq-mkempbuf (previous step)

subarray(buf, m, n0 + n1) = mkempbuf(n), m + n0 + n1 ≤ # buf ⊦ subarray(buf, m, n0) = mkempbuf(n0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ buf = buf0 ↔ # buf = # buf0 ∧ (∀ n. n < # buf → buf[n] = buf0[n])
Proof step 5:
# subarray(buf, m, n0 + n1) = # mkempbuf(n), m + n0 + n1 ≤ # buf, ∀ n2. n2 < # subarray(buf, m, n0 + n1) → subarray(buf, m, n0 + n1)[n2] = mkempbuf(n)[n2] ⊦ subarray(buf, m, n0) = mkempbuf(n0)

Rule argument

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

Additional information

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