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Proof step 42 from proof decode (previous step)

# vtbl1 = m0 + 1, err = ESUCCESS, n0 = (ENCODED_NAT_SIZE + # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE)) + ENCODED_VOLID_SIZE, n5 = (m0 + 1) + # vtbl, is-encoded(v, subarray(buf, ENCODED_NAT_SIZE + # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), ENCODED_VOLID_SIZE)), is-encoded(vtbl0, buf), is-encoded((m0 + 1) + # vtbl, subarray(buf, 0, ENCODED_NAT_SIZE)), is-encoded-rec(vtbl, subarray(buf, ENCODED_NAT_SIZE, # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE))), is-encoded-rec (vtbl1, subarray (buf, ENCODED_NAT_SIZE + # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) * m0 + ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE)), ENCODED_NAT_SIZE + # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) + ENCODED_VOLID_SIZE ≤ # buf, 2 * ENCODED_NAT_SIZE + (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) * (m0 + # vtbl) + ENCODED_VOLID_SIZE ≤ # buf, vtbl ⊥ vtbl1, err = ESUCCESS → is-encoded(m, subarray(buf, (ENCODED_NAT_SIZE + # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE)) + ENCODED_VOLID_SIZE, ENCODED_NAT_SIZE)) ∧ 2 * ENCODED_NAT_SIZE + # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) + ENCODED_VOLID_SIZE ≤ # buf ∧ n2 = ENCODED_NAT_SIZE, err0 = ESUCCESS → ENCODED_NAT_SIZE ≤ # buf ∧ n3 = ENCODED_NAT_SIZE, err = ESUCCESS ∨ ⌊err⌋ , err0 = ESUCCESS ∨ ⌊err0⌋ ⊦ vtbl1 = ∅, (err = ESUCCESS ∨ ⌊err⌋ ) ∧ ( err = ESUCCESS → (∃ vtbl2. vtbl[v, m] ⊥ vtbl2 ∧ # vtbl2 + # vtbl[v, m] = n5 ∧ # vtbl2 = m0 ∧ ENCODED_NAT_SIZE + (# vtbl2 + # vtbl[v, m]) * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) ≤ # buf ∧ n0 + n2 = ENCODED_NAT_SIZE + # vtbl[v, m] * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) ∧ is-encoded(# vtbl2 + # vtbl[v, m], subarray(buf, 0, ENCODED_NAT_SIZE)) ∧ is-encoded-rec(vtbl[v, m], subarray(buf, ENCODED_NAT_SIZE, # vtbl[v, m] * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE))) ∧ is-encoded-rec (vtbl2, subarray (buf, ENCODED_NAT_SIZE + # vtbl[v, m] * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), # vtbl2 * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE))))) ∧ m0 < # vtbl1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 43:
# vtbl1 = m0 + 1, is-encoded(m, subarray(buf, (ENCODED_NAT_SIZE + # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE)) + ENCODED_VOLID_SIZE, ENCODED_NAT_SIZE)), is-encoded(v, subarray(buf, ENCODED_NAT_SIZE + # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), ENCODED_VOLID_SIZE)), is-encoded(vtbl0, buf), is-encoded((m0 + 1) + # vtbl, subarray(buf, 0, ENCODED_NAT_SIZE)), is-encoded-rec(vtbl, subarray(buf, ENCODED_NAT_SIZE, # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE))), is-encoded-rec (vtbl1, subarray (buf, ENCODED_NAT_SIZE + # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) * m0 + ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE)), 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) + ENCODED_VOLID_SIZE ≤ # buf, 2 * ENCODED_NAT_SIZE + (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) * (m0 + # vtbl) + ENCODED_VOLID_SIZE ≤ # buf, vtbl ⊥ vtbl1, err0 = ESUCCESS → ENCODED_NAT_SIZE ≤ # buf ∧ n3 = ENCODED_NAT_SIZE, err0 = ESUCCESS ∨ ⌊err0⌋ ⊦ vtbl1 = ∅, ∃ vtbl2. vtbl[v, m] ⊥ vtbl2 ∧ # vtbl[v, m] = 1 + # vtbl ∧ # vtbl2 = m0 ∧ ENCODED_NAT_SIZE + (# vtbl2 + # 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 (vtbl2, subarray (buf, ENCODED_NAT_SIZE + # vtbl[v, m] * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), # vtbl2 * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE)))

Rule argument

Additional information

Used simplifier rules: ⊦ ¬ n < n; (s)% ⊦ m < n + 1 ↔ ¬ n < m; (s)%mult-c: ⊦ m * n = n * m; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult% ⊦ m * n + n = m1 * n ↔ m + 1 = m1 ∨ n = 0; (s)% ⊦ # subarray(buf, m, n) = n; (s)%is-encoded-size: ⊦ is-encoded(n, buf) → # buf = ENCODED_NAT_SIZE; (forward) from specification encoding-fixed-size[encoding-nat]% ⊦ is-encoded(n, buf) → (is-encoded(n0, buf) ↔ n = n0); (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)