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Proof step 26 from proof prepost-decode-orphans (previous step)

# 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) = ∅)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 27:
# buf = # orphans1 * 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, ENCODED_NAT_SIZE * m2)) ∧ orphans ∩ (orphans0 ++ n) = ∅)

Rule argument

Additional information

Used simplifier rules: eqs: ⊦ m = n + n0 ∧ m = n + n1 → n0 = n1; (forward) from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic