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Proof step 41 from proof is-encoded-split-one (previous step)

# buf = m * ENCODED_NAT_SIZE, # buf2 = ENCODED_NAT_SIZE, # buf1 = ENCODED_NAT_SIZE, # ns = m + 1, m + 1 = #((ns -- n0) ++ n), is-encoded(n0, buf2), is-encoded(ns -- n0, buf), is-encoded(n, buf1), is-encoded((ns -- n0) ++ n, buf + buf1), n0 ∈ ns, ∀ ns0, buf0, ns2, buf1, n0. # ns0 < #(ns ++ n) → # buf0 = # ns2 * ENCODED_NAT_SIZE ∧ # buf1 = ENCODED_NAT_SIZE ∧ is-encoded(n0, buf1) ∧ is-encoded(ns2, buf0) → (is-encoded(ns0, buf0 + buf1) ↔ ns0 = ns2 ++ n0) ∨ n0 ∈ ns2 ⊦ ns = ∅, n ∈ ns, ∃ n0, buf4, buf3. (n0 = n ∨ n0 ∈ ns) ∧ (buf2 + buf) + buf1 = buf4 + buf3 ∧ is-encoded(n0, buf4) ∧ is-encoded((ns ++ n) -- n0, buf3)

User applied rule exists right

And obtained the following new goals

Proof step 42:
# ns = m + 1, # buf1 = ENCODED_NAT_SIZE, # buf2 = ENCODED_NAT_SIZE, # buf = m * ENCODED_NAT_SIZE, m + 1 = #((ns -- n0) ++ n), is-encoded((ns -- n0) ++ n, buf + buf1), is-encoded(n, buf1), is-encoded(ns -- n0, buf), is-encoded(n0, buf2), n0 ∈ ns, ∀ ns0, buf0, ns2, buf1, n0. # ns0 < #(ns ++ n) → # buf0 = # ns2 * ENCODED_NAT_SIZE ∧ # buf1 = ENCODED_NAT_SIZE ∧ is-encoded(n0, buf1) ∧ is-encoded(ns2, buf0) → (is-encoded(ns0, buf0 + buf1) ↔ ns0 = ns2 ++ n0) ∨ n0 ∈ ns2 ⊦ ns = ∅, n ∈ ns, (n0 = n ∨ n0 ∈ ns) ∧ (buf2 + buf) + buf1 = buf2 + buf + buf1 ∧ is-encoded(n0, buf2) ∧ is-encoded((ns ++ n) -- n0, buf + buf1)

Rule argument

pos: right 3 terms: n0, buf2, buf + buf1 abort: F discard: T computed: F

Additional information

Used terms: n0, buf2, buf + buf1