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Proof step 7 from proof is-encoded-unique (previous step)

# buf0 = EB_PAGE_SIZE, # buf = EB_PAGE_SIZE, buf0 + buf1 = buf + buf2, is-encoded(nx, buf1), is-encoded(rnode(m), buf0), is-encoded(rnode(m0), buf), is-encoded(nx1, buf2), ∀ nx0, buf. is-encoded(nx0, buf) ∧ is-encoded(nx, buf) → nx0 = nx ⊦ m0 ' + nx1 = m ' + nx

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ # buf = # buf0 → (buf + buf1 = buf0 + buf2 ↔ buf = buf0 ∧ buf1 = buf2)
Proof step 9:
# buf = EB_PAGE_SIZE, # buf0 = EB_PAGE_SIZE, # buf0 = # buf, buf0 = buf, buf1 = buf2, is-encoded(nx1, buf2), is-encoded(rnode(m0), buf), is-encoded(rnode(m), buf0), is-encoded(nx, buf1), ∀ nx0, buf. is-encoded(nx0, buf) ∧ is-encoded(nx, buf) → nx0 = nx ⊦ m0 ' + nx1 = m ' + nx

Rule argument

spec: array-splice, inst: buffer name: append-inj seq: ⊦ # buf = # buf0 → (buf + buf1 = buf0 + buf2 ↔ buf = buf0 ∧ buf1 = buf2) subst: [buf2, buf0, buf1, buf] → [buf2, buf, buf1, buf0] flags: <all paths>

Additional information

Used terms: buf2, buf, buf1, buf0