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Proof step 69 from proof decode (previous step)

# 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), 2 * ENCODED_NAT_SIZE + (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) * # vtbl = n1 + # buf4, n1 = n0 + 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, ENCODED_NAT_SIZE ≤ n1, # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) ≤ # buf4 + # buf0 + # buf3, ENCODED_NAT_SIZE + (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) * (m0 + # vtbl) ≤ # buf4 + # buf0 + # buf3, n1 ≤ ENCODED_NAT_SIZE + # 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(buf0 + buf3, n0, # buf0))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 70:
# buf0 = m0 * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), # vtbl1 = m0 + 1, # buf2 = ENCODED_VOLID_SIZE, # buf1 = ENCODED_NAT_SIZE, ENCODED_NAT_SIZE + (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) * # vtbl = # buf4, is-encoded((m0 + 1) + # vtbl, subarray(buf4, 0, ENCODED_NAT_SIZE)), is-encoded(vtbl0, buf4 + (buf2 + buf1 + buf0) + buf3), is-encoded(vtbl1[v], buf1), is-encoded(v, buf2), is-encoded-rec(vtbl, subarray(buf4, ENCODED_NAT_SIZE, # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE))), is-encoded-rec(vtbl1 -- v, buf0), v ∈ vtbl1, ENCODED_NAT_SIZE + (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) * (m0 + # vtbl) ≤ # buf4 + # buf0 + # buf3, # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) ≤ # buf4 + # buf0 + # buf3, vtbl ⊥ vtbl1, err0 = ESUCCESS → n3 = ENCODED_NAT_SIZE, err0 = ESUCCESS ∨ ⌊err0⌋ ⊦ vtbl1 = ∅, 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)), v ∈ vtbl

Rule argument

Additional information

Used simplifier rules: is-encoded-rec-unique: ⊦ is-encoded-rec(vtbl0, buf) → (is-encoded-rec(vtbl1, buf) ↔ vtbl0 = vtbl1);%# buf = n ⊦ subarray(buf, 0, n) = buf; (s)% ⊦ 0 ≤ m; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[encoding-nat-buffer]%n + m ≤ # buf ⊦ subarray(buf + buf0, n, m) = subarray(buf, n, m); (s)% ⊦ ¬ n < n; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ n + 0 = n; (s)% ⊦ m = m + n ↔ n = 0; (s)% ⊦ m ≤ m + n; (s)% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%mult-c: ⊦ m * n = n * m; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult% ⊦ m0 * 1 = m0; (s)%m2 ≠ 0 ⊦ (* m2) * m + n = m + n0 ↔ (m2 - 1) * m + n = n0; (s)