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Proof step 20 from proof prepost-encode-orphans (previous step)

# buf0 = # buf, subarray(buf0, m0 + ENCODED_NAT_SIZE, # buf - m0 + ENCODED_NAT_SIZE) = subarray(buf, m0 + ENCODED_NAT_SIZE, # buf - m0 + ENCODED_NAT_SIZE), subarray(buf0, 0, m0) = subarray(buf, 0, m0), is-aligned(# buf, EB_PAGE_SIZE), is-encoded(n, subarray(buf0, m0, ENCODED_NAT_SIZE)), is-encoded(orphans2 \ orphans1, subarray(buf, 0, m0)), n ∈ orphans2, n ∈ orphans1, m0 + ENCODED_NAT_SIZE ≤ LEB_SIZE, m0 + ENCODED_NAT_SIZE ≤ # buf, m0 + # orphans1 * ENCODED_NAT_SIZE ≤ LEB_SIZE, m0 + # orphans1 * ENCODED_NAT_SIZE ≤ # buf, # orphans2 * ENCODED_NAT_SIZE ≤ LEB_SIZE, # buf ≤ LEB_SIZE, orphans1 ⊆ orphans2 ⊦ # orphans1 = 0, # orphans2 = 0, orphans1 = ∅, orphans2 = ∅, m0 + ENCODED_NAT_SIZE + (# orphans1 - 1) * ENCODED_NAT_SIZE ≤ # buf ∧ is-encoded((orphans2 \ orphans1) ++ n, subarray(buf0, 0, m0 + ENCODED_NAT_SIZE))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 21:
# buf0 = # buf, # orphans1 = m + 1, subarray(buf0, 0, m0) = subarray(buf, 0, m0), subarray(buf0, m0 + ENCODED_NAT_SIZE, # buf - m0 + ENCODED_NAT_SIZE) = subarray(buf, m0 + ENCODED_NAT_SIZE, # buf - m0 + ENCODED_NAT_SIZE), is-aligned(# buf, EB_PAGE_SIZE), is-encoded(orphans2 \ orphans1, subarray(buf, 0, m0)), is-encoded(n, subarray(buf0, m0, ENCODED_NAT_SIZE)), n ∈ orphans1, n ∈ orphans2, # buf ≤ LEB_SIZE, # orphans2 * ENCODED_NAT_SIZE ≤ LEB_SIZE, m0 + # orphans1 * ENCODED_NAT_SIZE ≤ # buf, m0 + # orphans1 * ENCODED_NAT_SIZE ≤ LEB_SIZE, m0 + ENCODED_NAT_SIZE ≤ # buf, m0 + ENCODED_NAT_SIZE ≤ LEB_SIZE, orphans1 ⊆ orphans2 ⊦ # orphans2 = 0, # orphans1 = 0, orphans1 = ∅, orphans2 = ∅, m0 + ENCODED_NAT_SIZE + m * ENCODED_NAT_SIZE ≤ # buf ∧ is-encoded((orphans2 \ orphans1) ++ n, subarray(buf0, 0, m0 + ENCODED_NAT_SIZE))

Rule argument

spec: nat name: elim-pred-c seq: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1 subst: [n, m] → [# orphans1, m1]

Additional information

Used simplifier rules: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1; (elim) Used terms: # orphans1, m1