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Proof step 29 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, m + ENCODED_NAT_SIZE ≤ # buf → (∃ buf0, buf1, buf2. buf = buf0 + buf1 + buf2 ∧ # buf0 = m ∧ # buf1 = ENCODED_NAT_SIZE) ⊦ 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) = ∅)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 30:
# buf1 = ENCODED_NAT_SIZE, ENCODED_NAT_SIZE * m2 = # buf2, # buf0 + ENCODED_NAT_SIZE + ENCODED_NAT_SIZE * m2 = # orphans1 * ENCODED_NAT_SIZE, orphans ∩ orphans0 = ∅, is-encoded(orphans, buf1 + buf2), is-encoded(orphans0, buf0), is-encoded(orphans1, buf0 + buf1 + buf2), is-encoded(n, buf1) ⊦ is-encoded(orphans0 ++ n, buf0 + buf1) ∧ (∃ orphans2. is-encoded(orphans2, buf2) ∧ orphans2 ∩ (orphans0 ++ n) = ∅)

Rule argument

Additional information

Used simplifier rules: ⊦ m - m = 0; (s)% ⊦ m ≤ m; (s)% ⊦ m + n - m = n; (s)%# buf ≤ n0, n0 + m ≤ # buf + # buf0 ⊦ subarray(buf + buf0, n0, m) = subarray(buf0, n0 - # buf, m); (s)% ⊦ m + n < m + n0 ↔ n < n0; (s)% ⊦ m < n → n ≠ 0; (s)%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat%int-c: ⊦ ns ∩ ns0 = ns0 ∩ ns; from specification set-union[nat-set]%int-a: ⊦ (ns ∩ ns0) ∩ ns1 = ns ∩ ns0 ∩ ns1; from specification set-union[nat-set]% ⊦ ns ∩ (ns0 ++ n) = ∅ ↔ ns ∩ ns0 = ∅ ∧ ¬ n ∈ ns; (ws)% ⊦ m ≤ m + n; (s)%m ≤ # buf ⊦ subarray(buf0 + buf, 0, # buf0 + m) = buf0 + subarray(buf, 0, m); (s)% ⊦ m ≤ n → (n < m ↔ false); (s)%# buf = n ⊦ subarray(buf, 0, n) = buf; (s)% ⊦ ¬ n < n; (s)% ⊦ ENCODED_NAT_SIZE ≠ 0; (s)%is-encoded-size: ⊦ is-encoded(n, buf) → # buf = ENCODED_NAT_SIZE; (forward) from specification encoding-fixed-size[encoding-nat]%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%n = # buf ⊦ subarray(buf + buf0, 0, n) = buf; (s)%m ≤ # buf ⊦ subarray(buf0 + buf, # buf0, m) = subarray(buf, 0, m); (s)% ⊦ m < n → (n ≤ m ↔ false); (s)% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + n = m + n0 ↔ n = n0; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ #(buf + buf0) = # buf + # buf0; (s)