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Proof step 7 from proof ls-datasize-zero (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ buf = buf0 ↔ # buf = # buf0 ∧ (∀ n. n < # buf → buf[n] = buf0[n])
Proof step 9:
# buf = n1 + n, ∀ n0. n0 < n → buf[n0] = empty ⊦ # buf = #(mkempbuf(n) + subarray(buf, n, n1)) ∧ (∀ n0. n0 < # buf → buf[n0] = (mkempbuf(n) + subarray(buf, n, n1))[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, n, n1), buf] flags: <all paths>

Additional information

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