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

buf1 = mkempbuf(# buf1), m0 ≤ # buf1 ⊦ # buf0 + datasize(buf1, m0) = datasize(buf0, # buf0), datasize(buf1, m0) = 0, m0 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ datasize(buf, m) = 0 ↔ (∀ n. n < m → buf[n] = empty)
Proof step 11:
buf1 = mkempbuf(# buf1), m0 ≤ # buf1 ⊦ # buf0 + datasize(buf1, m0) = datasize(buf0, # buf0), m0 = 0, ∀ n. n < m0 → buf1[n] = empty

Rule argument

spec: <toplevel> name: datasize-zero-h seq: ⊦ datasize(buf, m) = 0 ↔ (∀ n. n < m → buf[n] = empty) subst: [m, buf] → [m0, buf1] flags: <all paths>

Additional information

Used terms: m0, buf1