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Proof step 53 from proof decode (previous step)

# buf0 = m0 * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), # vtbl1 = m0 + 1, # buf2 = ENCODED_VOLID_SIZE, # buf1 = ENCODED_NAT_SIZE, is-encoded((m0 + 1) + # vtbl, subarray(buf, 0, ENCODED_NAT_SIZE)), is-encoded(vtbl0, buf), is-encoded(v, subarray(buf, ENCODED_NAT_SIZE + # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), ENCODED_VOLID_SIZE)), is-encoded(m, subarray(buf, (ENCODED_NAT_SIZE + # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE)) + ENCODED_VOLID_SIZE, ENCODED_NAT_SIZE)), is-encoded(vtbl1[v0], buf1), is-encoded(v0, buf2), is-encoded-rec(vtbl, subarray(buf, ENCODED_NAT_SIZE, # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE))), is-encoded-rec(vtbl1 -- v0, buf0), v0 ∈ vtbl1, 2 * ENCODED_NAT_SIZE + (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) * (m0 + # vtbl) + ENCODED_VOLID_SIZE ≤ # buf, ENCODED_NAT_SIZE + # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) + ENCODED_VOLID_SIZE ≤ # buf, 2 * ENCODED_NAT_SIZE + # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) + ENCODED_VOLID_SIZE ≤ # buf, (ENCODED_NAT_SIZE + # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE)) + # buf0 + ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE ≤ # buf, vtbl ⊥ vtbl1, err0 = ESUCCESS → ENCODED_NAT_SIZE ≤ # buf ∧ n3 = ENCODED_NAT_SIZE, ∃ buf4, buf3. buf = buf4 + (buf2 + buf1 + buf0) + buf3 ∧ # buf4 = ENCODED_NAT_SIZE + # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) ∧ #(buf2 + buf1 + buf0) = # buf0 + ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE, err0 = ESUCCESS ∨ ⌊err0⌋ ⊦ vtbl1 = ∅, v0 ∈ vtbl, # vtbl[v, m] = 1 + # vtbl ∧ #(vtbl1 -- v) = m0 ∧ ENCODED_NAT_SIZE + (#(vtbl1 -- v) + # vtbl[v, m]) * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) ≤ # buf ∧ is-encoded-rec(vtbl[v, m], subarray(buf, ENCODED_NAT_SIZE, # vtbl[v, m] * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE))) ∧ is-encoded-rec (vtbl1 -- v, subarray (buf, ENCODED_NAT_SIZE + # vtbl[v, m] * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), #(vtbl1 -- v) * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE)))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 54:
# buf1 = ENCODED_NAT_SIZE, # buf2 = ENCODED_VOLID_SIZE, # vtbl1 = m0 + 1, # buf0 = m0 * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), # buf4 = ENCODED_NAT_SIZE + # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), is-encoded(v, buf2), is-encoded(vtbl1[v], buf1), is-encoded(vtbl0, buf4 + (buf2 + buf1 + buf0) + buf3), is-encoded((m0 + 1) + # vtbl, subarray(buf4, 0, ENCODED_NAT_SIZE)), is-encoded-rec(vtbl1 -- v, buf0), is-encoded-rec(vtbl, subarray(buf4, ENCODED_NAT_SIZE, # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE))), v ∈ vtbl1, # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) ≤ # buf4 + # buf0 + # buf3, ENCODED_NAT_SIZE + (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) * (m0 + # vtbl) ≤ # buf4 + # buf0 + # buf3, vtbl ⊥ vtbl1, err0 = ESUCCESS → n3 = ENCODED_NAT_SIZE, err0 = ESUCCESS ∨ ⌊err0⌋ ⊦ vtbl1 = ∅, v ∈ vtbl, is-encoded-rec (vtbl[v, vtbl1[v]], subarray (buf4 + (buf2 + buf1 + buf0) + buf3, ENCODED_NAT_SIZE, (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) * # vtbl + ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE)) ∧ is-encoded-rec (vtbl1 -- v, subarray (buf2 + buf1 + buf0 + buf3, 2 * ENCODED_NAT_SIZE + (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) * # vtbl + ENCODED_VOLID_SIZE - # buf4, # buf0))

Rule argument

Additional information

Used simplifier rules: is-encoded-rec-size: ⊦ is-encoded-rec(vtbl, buf) → # buf = # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE);% ⊦ n ≤ m → m + n0 - n = (m - n) + n0; (s)%disjoint-in-right: ⊦ v ∈ vtbl ∧ vtbl0 ⊥ vtbl → ¬ v ∈ vtbl0; (forward) from specification store-union[vtbl]% ⊦ n -1 = n - 1; (s)% ⊦ v ∈ vtbl → #(vtbl -- v) = (# vtbl)-1; (s)% ⊦ ¬ v ∈ vtbl → # vtbl[v, n] = # vtbl + 1; (s)% ⊦ m0 * 1 = m0; (s)%m2 ≠ 0 ⊦ (* m2) * m + n ≤ m + n0 ↔ (m2 - 1) * m + n ≤ n0; (s)% ⊦ is-encoded(n, buf) → (is-encoded(n0, buf) ↔ n = n0); (s)% ⊦ is-encoded(v, buf) → (is-encoded(v0, buf) ↔ v = v0); (s)%# buf = n ⊦ subarray(buf, 0, n) = buf; (s)% ⊦ m * n + n0 < n ↔ m = 0 ∧ n0 < n; (ws)% ⊦ m * (n + 1) = m * n + m; (s)%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic% ⊦ ENCODED_VOLID_SIZE ≠ 0; (s)% ⊦ n + 0 = n; (s)% ⊦ m - m = 0; (s)% ⊦ ENCODED_NAT_SIZE ≠ 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; (s)% ⊦ m + n < m + n0 ↔ n < n0; (s)% ⊦ m < n → n ≠ 0; (s)%mult-c: ⊦ m * n = n * m; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult% ⊦ m0 ≠ 0 → (m * m0 = n * m0 ↔ m = n); (s)% ⊦ # subarray(buf, m, n) = n; (s)%is-encoded-size: ⊦ is-encoded(v, buf) → # buf = ENCODED_VOLID_SIZE; (forward) from specification encoding-fixed-size[encoding-volid]%is-encoded-size: ⊦ is-encoded(n, buf) → # buf = ENCODED_NAT_SIZE; (forward) from specification encoding-fixed-size[encoding-nat]%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m ≤ m + n; (s)%n + m ≤ # buf ⊦ subarray(buf + buf0, n, m) = subarray(buf, n, m); (s)% ⊦ ¬ n < n; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)% ⊦ m + m = 2 * m; (s)%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[encoding-nat-buffer]% ⊦ #(buf + buf0) = # buf + # buf0; (s)