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Proof step 8 from proof is-encoded-unique (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 9:
# buf1 = ENCODED_NAT_SIZE, # buf0 = m * ENCODED_NAT_SIZE, # ns0 = m + 1, # ns1 * ENCODED_NAT_SIZE = # ns0 * ENCODED_NAT_SIZE, ENCODED_NAT_SIZE + # buf0 = # ns0 * ENCODED_NAT_SIZE, is-encoded(ns1, buf1 + buf0), is-encoded(ns0 -- n, buf0), is-encoded(n, buf1), n ∈ ns0, ∀ ns, buf, ns1. # ns < # ns0 → # buf = # ns1 * ENCODED_NAT_SIZE ∧ # buf = # ns * ENCODED_NAT_SIZE ∧ is-encoded(ns, buf) ∧ is-encoded(ns1, buf) → ns = ns1 ⊦ # ns0 = 0, ns0 = ns1, ns0 = ∅

Rule argument

spec: nat name: elim-pred-c seq: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1 subst: [n, m] → [# ns0, m]

Additional information

Used simplifier rules: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1; (elim) Used terms: # ns0, m