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Proof step 12 from proof datasize-split-empty-h (previous step)

buf1 = mkempbuf(# buf1), n < m0, n < # buf1, m0 ≤ # buf1 ⊦ # buf0 + datasize(buf1, m0) = datasize(buf0, # buf0), buf1[n] = empty

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ buf = buf0 ↔ # buf = # buf0 ∧ (∀ n. n < # buf → buf[n] = buf0[n])
Proof step 14:
# buf1 = # mkempbuf(# buf1), n < # buf1, n < m0, m0 ≤ # buf1, ∀ n. n < # buf1 → buf1[n] = mkempbuf(# buf1)[n] ⊦ # buf0 + datasize(buf1, m0) = datasize(buf0, # buf0), buf1[n] = empty

Rule argument

spec: array, inst: buffer name: Extension seq: ⊦ buf = buf0 ↔ # buf = # buf0 ∧ (∀ n. n < # buf → buf[n] = buf0[n]) subst: [buf0, buf] → [mkempbuf(# buf1), buf1] flags: <all paths>

Additional information

Used terms: mkempbuf(# buf1), buf1