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Proof step 12 from proof prepost-decode-orphans (previous step)

# buf = # orphans1 * ENCODED_NAT_SIZE, m + m1 * ENCODED_NAT_SIZE = # buf, m1 = m2 + 1, orphans ∩ orphans0 = ∅, is-encoded(orphans, subarray(buf, m, # buf - m)), is-encoded(orphans0, subarray(buf, 0, m)), is-encoded(orphans1, buf) ⊦ ⟪decode_nat#(m, buf; n, m0; err); if err = ESUCCESS then orphans0 := orphans0 ++ n; m := m + ENCODED_NAT_SIZE; m4 := m2⟫ ( (err = ESUCCESS ∨ ⌊err⌋ ) ∧ m + m4 * ENCODED_NAT_SIZE = # buf ∧ ( err = ESUCCESS → is-encoded(orphans0, subarray(buf, 0, m)) ∧ (∃ orphans. is-encoded(orphans, subarray(buf, m, # buf - m)) ∧ orphans ∩ orphans0 = ∅)) ∧ m4 < m1), m1 = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
# buf = # orphans1 * ENCODED_NAT_SIZE, m + ENCODED_NAT_SIZE * m2 + ENCODED_NAT_SIZE = # buf, orphans ∩ orphans0 = ∅, is-encoded(orphans1, buf), is-encoded(orphans0, subarray(buf, 0, m)), is-encoded(orphans, subarray(buf, m, # buf - m)) ⊦ ⟪decode_nat#(m, buf; n, m0; err); if err = ESUCCESS then orphans0 := orphans0 ++ n; m := m + ENCODED_NAT_SIZE; m4 := m2⟫ ( (err = ESUCCESS ∨ ⌊err⌋ ) ∧ m + m4 * ENCODED_NAT_SIZE = # buf ∧ ( err = ESUCCESS → is-encoded(orphans0, subarray(buf, 0, m)) ∧ (∃ orphans. is-encoded(orphans, subarray(buf, m, # buf - m)) ∧ orphans ∩ orphans0 = ∅)) ∧ ¬ m2 < m4)

Rule argument

Additional information

Used simplifier rules: ⊦ m < n + 1 ↔ ¬ n < m; (s)% ⊦ m + 1 ≠ 0; (s)%mult-c: ⊦ m * n = n * m; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m * (n + 1) = m * n + m; (s)