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Proof step 11 from proof is-encoded-split-one (previous step)

# buf = m * ENCODED_NAT_SIZE, # buf2 = ENCODED_NAT_SIZE, # buf0 = # ns * ENCODED_NAT_SIZE, # buf1 = ENCODED_NAT_SIZE, # ns1 = m + 1, buf0 + buf1 = buf2 + buf, is-encoded(n0, buf2), is-encoded(ns1 -- n0, buf), is-encoded(n, buf1), is-encoded(ns, buf0), n0 ∈ ns1, ∀ ns0, buf0, ns, buf1, n. # ns0 < # ns1 → # buf0 = # ns * ENCODED_NAT_SIZE ∧ # buf1 = ENCODED_NAT_SIZE ∧ is-encoded(n, buf1) ∧ is-encoded(ns, buf0) → (is-encoded(ns0, buf0 + buf1) ↔ ns0 = ns ++ n) ∨ n ∈ ns ⊦ # ns1 = 0, ns1 = ns ++ n, ns1 = ∅, n ∈ ns

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
# buf = m * ENCODED_NAT_SIZE, # buf2 = ENCODED_NAT_SIZE, # buf0 = # ns * ENCODED_NAT_SIZE, # buf1 = ENCODED_NAT_SIZE, # ns1 = m + 1, buf0 + buf1 = buf2 + buf, is-encoded(n0, buf2), is-encoded(ns1 -- n0, buf), is-encoded(n, buf1), is-encoded(ns, buf0), n0 ∈ ns1, ∀ ns0, buf0, ns, buf1, n. # ns0 < m + 1 → # buf0 = # ns * ENCODED_NAT_SIZE ∧ # buf1 = ENCODED_NAT_SIZE ∧ is-encoded(n, buf1) ∧ is-encoded(ns, buf0) → (is-encoded(ns0, buf0 + buf1) ↔ ns0 = ns ++ n) ∨ n ∈ ns ⊦ ns1 = ns ++ n, ns1 = ∅, n ∈ ns

Rule argument

Additional information

Used simplifier rules: c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + 1 ≠ 0; (s)