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Proof step 9 from proof datasize-add-empty-h (previous step)

buf[n0 + n] = empty, subarray(buf, n0, n + 1) = mkempbuf(n + 1), n0 + n < # buf ⊦ datasize(buf, n0 + n) = datasize(buf, n0), subarray(buf, n0, n) = mkempbuf(n)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ buf = buf0 ↔ # buf = # buf0 ∧ (∀ n. n < # buf → buf[n] = buf0[n])
Proof step 11:
# subarray(buf, n0, n + 1) = # mkempbuf(n + 1), buf[n0 + n] = empty, n0 + n < # buf, ∀ n1. n1 < # subarray(buf, n0, n + 1) → subarray(buf, n0, n + 1)[n1] = mkempbuf(n + 1)[n1] ⊦ datasize(buf, n0 + n) = datasize(buf, n0), subarray(buf, n0, n) = mkempbuf(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(n + 1), subarray(buf, n0, n + 1)] flags: <all paths>

Additional information

Used terms: mkempbuf(n + 1), subarray(buf, n0, n + 1)