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Proof step 11 from proof prepost-decode-orphans (previous step)

# buf = # orphans1 * ENCODED_NAT_SIZE, m + m1 * ENCODED_NAT_SIZE = # buf, orphans ∩ orphans0 = ∅, m1 ≠ 0, 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 := m1 - 1⟫ ( (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)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 12:
# 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

Rule argument

spec: nat name: elim-pred-c seq: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1 subst: [n, m] → [m1, m2]

Additional information

Used simplifier rules: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1; (elim) Used terms: m1, m2