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Proof step 24 from proof is-encoded-split-one (previous step)

# ns1 = 2 + m0, # buf3 = m0 * ENCODED_NAT_SIZE, # ns = m0 + 1, # buf2 = ENCODED_NAT_SIZE, # buf1 = ENCODED_NAT_SIZE, m0 + 1 = #((ns -- n1) ++ n), ns1 -- n1 = (ns -- n1) ++ n, is-encoded(ns -- n1, buf3), is-encoded(n1, buf2), is-encoded((ns -- n1) ++ n, buf3 + buf1), is-encoded(n, buf1), n ∈ ns1, n1 ∈ ns1, n1 ∈ ns, ∀ ns0, buf0, ns, buf1, n. # ns0 < (m0 + 1) + 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 ⊦ ns = ∅, ns1 = ∅, n ∈ ns, ∀ n0. n0 ∈ ns1 ↔ n0 ∈ ns ++ n

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 25:
# buf1 = ENCODED_NAT_SIZE, # buf2 = ENCODED_NAT_SIZE, # ns = m0 + 1, # buf3 = m0 * ENCODED_NAT_SIZE, # ns1 = 2 + m0, m0 + 1 = #((ns -- n1) ++ n), ns1 -- n1 = (ns -- n1) ++ n, is-encoded(n, buf1), is-encoded((ns -- n1) ++ n, buf3 + buf1), is-encoded(n1, buf2), is-encoded(ns -- n1, buf3), n1 ∈ ns, n1 ∈ ns1, n ∈ ns1, ∀ ns0, buf0, ns, buf1, n. # ns0 < (m0 + 1) + 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 ⊦ n0 ∈ ns1 ↔ n0 = n ∨ n0 ∈ ns, ns = ∅, ns1 = ∅, n ∈ ns

Rule argument

Additional information

Used simplifier rules: ⊦ n ∈ ns ++ n0 ↔ n = n0 ∨ n ∈ ns; (s)