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Proof step 12 from proof is-encoded-emptypage-middle (previous step)

# buf0 = EB_PAGE_SIZE, buf + emptypage + buf1 = buf0 + buf2, is-aligned(# buf, EB_PAGE_SIZE), is-encoded(nx0, buf2), is-encoded(rnode(m), buf0), EB_PAGE_SIZE ≤ # buf, # buf ≠ 0 → buf = buf3 + buf4 ∧ # buf3 = EB_PAGE_SIZE, ∀ buf3, buf4. ¬ is-aligned(# buf3, EB_PAGE_SIZE) ∨ ¬ is-encoded(nx0, buf3 + emptypage + buf4) ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
# buf0 = EB_PAGE_SIZE, # buf3 = EB_PAGE_SIZE, (buf3 + buf4) + emptypage + buf1 = buf0 + buf2, is-aligned(# buf4, EB_PAGE_SIZE), is-encoded(rnode(m), buf0), is-encoded(nx0, buf2), ∀ buf3, buf4. ¬ is-aligned(# buf3, EB_PAGE_SIZE) ∨ ¬ is-encoded(nx0, buf3 + emptypage + buf4) ⊦

Rule argument

Additional information

Used simplifier rules: ⊦ EB_PAGE_SIZE + n = 0 ↔ false; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%m ≠ 0, is-aligned(n1, m) ⊦ is-aligned(n0 + n1, m) ↔ is-aligned(n0, m); (s)%n ≠ 0 ⊦ is-aligned(n, n); (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ #(buf + buf0) = # buf + # buf0; (s)%m ≠ 0 ⊦ is-aligned(n, m) → (m ≤ n ↔ n ≠ 0); (s)% ⊦ EB_PAGE_SIZE ≠ 0; (s)