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Proof step 18 from proof is-encoded-split-one (previous step)

# buf3 = (# ns - 1) * ENCODED_NAT_SIZE, # ns1 = m + 1, # buf1 = ENCODED_NAT_SIZE, # buf2 = ENCODED_NAT_SIZE, # ns * ENCODED_NAT_SIZE = m * ENCODED_NAT_SIZE, ENCODED_NAT_SIZE + # buf3 = m * ENCODED_NAT_SIZE, is-encoded(n, buf1), is-encoded(ns1 -- n1, buf3 + buf1), is-encoded(n1, buf2), is-encoded(ns -- n1, buf3), n1 ∈ ns, n1 ∈ 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 ⊦ # ns = 0, ns = ∅, ns1 = ∅, ns1 = ns ++ n, n ∈ ns

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 19:
# buf2 = ENCODED_NAT_SIZE, # buf1 = ENCODED_NAT_SIZE, # ns1 = m + 1, # buf3 = m0 * ENCODED_NAT_SIZE, # ns = m0 + 1, # ns * ENCODED_NAT_SIZE = m * ENCODED_NAT_SIZE, ENCODED_NAT_SIZE + # buf3 = m * ENCODED_NAT_SIZE, is-encoded(ns -- n1, buf3), is-encoded(n1, buf2), is-encoded(ns1 -- n1, buf3 + buf1), is-encoded(n, buf1), n1 ∈ ns1, n1 ∈ ns, ∀ 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 ⊦ # ns = 0, ns = ∅, ns1 = ns ++ n, ns1 = ∅, n ∈ ns

Rule argument

spec: nat name: elim-pred-c seq: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1 subst: [n, m] → [# ns, m0]

Additional information

Used simplifier rules: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1; (elim) Used terms: # ns, m0