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Proof step 25 from proof prepost-decode-orphans (previous step)

# buf = # orphans1 * ENCODED_NAT_SIZE, (ENCODED_NAT_SIZE * m2 + ENCODED_NAT_SIZE) + m = # buf, orphans ∩ orphans0 = ∅, is-encoded(n, subarray(buf, m, ENCODED_NAT_SIZE)), is-encoded(orphans1, buf), is-encoded(orphans0, subarray(buf, 0, m)), is-encoded(orphans, subarray(buf, m, ENCODED_NAT_SIZE * m2 + ENCODED_NAT_SIZE)), m + ENCODED_NAT_SIZE ≤ # buf ⊦ is-encoded(orphans0 ++ n, subarray(buf, 0, m + ENCODED_NAT_SIZE)) ∧ (∃ orphans. is-encoded(orphans, subarray(buf, m + ENCODED_NAT_SIZE, # buf - m + ENCODED_NAT_SIZE)) ∧ orphans ∩ (orphans0 ++ n) = ∅)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 26:
# buf = # orphans1 * ENCODED_NAT_SIZE, # buf = n0 + m + ENCODED_NAT_SIZE, (ENCODED_NAT_SIZE * m2 + ENCODED_NAT_SIZE) + m = # buf, orphans ∩ orphans0 = ∅, is-encoded(orphans, subarray(buf, m, ENCODED_NAT_SIZE * m2 + ENCODED_NAT_SIZE)), is-encoded(orphans0, subarray(buf, 0, m)), is-encoded(orphans1, buf), is-encoded(n, subarray(buf, m, ENCODED_NAT_SIZE)), m + ENCODED_NAT_SIZE ≤ # buf ⊦ is-encoded(orphans0 ++ n, subarray(buf, 0, m + ENCODED_NAT_SIZE)) ∧ (∃ orphans. is-encoded(orphans, subarray(buf, m + ENCODED_NAT_SIZE, n0)) ∧ orphans ∩ (orphans0 ++ n) = ∅)

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [m, n, n0] → [# buf, m + ENCODED_NAT_SIZE, n0]

Additional information

Used simplifier rules: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: # buf, m + ENCODED_NAT_SIZE, n0