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Proof step 15 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(orphans1, buf), is-encoded(orphans0, subarray(buf, 0, m)), is-encoded(orphans, subarray(buf, m, ENCODED_NAT_SIZE * m2 + ENCODED_NAT_SIZE)) ⊦ ⟪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)

User applied rule insert program lemma

And obtained the following new goals

Rule argument

spec: encoding, inst: encoding-nat name: decode-contract seq: ⊦ ⟪decode_nat#(n1, buf; n, n0; err)⟫ ( (err = ESUCCESS ∨ ⌊err⌋ ) ∧ ( err = ESUCCESS → is-encoded(n, subarray(buf, n1, n0)) ∧ n1 + n0 ≤ # buf ∧ n0 = encoding-size(n))) subst: [buf, n1, n0, n, err] → [buf, m, m0, n, err] flags: <all paths>

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