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Proof step 59 from proof decode (previous step)

# buf4 = ENCODED_NAT_SIZE + # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), # buf0 = m0 * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), # vtbl1 = m0 + 1, # buf2 = ENCODED_VOLID_SIZE, # buf1 = ENCODED_NAT_SIZE, 2 * ENCODED_NAT_SIZE + (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) * # vtbl + ENCODED_VOLID_SIZE = n0 + # 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 = ∅, 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, n0, # buf0)), ENCODED_VOLID_SIZE ≤ n0 ∧ n0 ≤ ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE + # buf3

User applied rule insert equation

And closed the goal!

Rule argument

pos: left 1 flags: discard

Additional information

Used simplifier rules: is-encoded-rec-size: ⊦ is-encoded-rec(vtbl, buf) → # buf = # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE);%is-encoded-rec-unique: ⊦ is-encoded-rec(vtbl0, buf) → (is-encoded-rec(vtbl1, buf) ↔ vtbl0 = vtbl1);%mult-c: ⊦ m * n = n * m; from specification nat-mult% ⊦ m + n = m + n0 ↔ n = n0; (s)%m2 ≠ 0 ⊦ (* m2) * m + n = m + n0 ↔ (m2 - 1) * m + n = n0; (s)% ⊦ m0 * 1 = m0; (s)%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)% ⊦ m ≤ m + n; (s)% ⊦ #(buf + buf0) = # buf + # buf0; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[encoding-nat-buffer]% ⊦ m ≤ n ↔ ¬ n < m; (ss)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic% ⊦ # subarray(buf, m, n) = n; (s)% ⊦ ¬ v ∈ vtbl → # vtbl[v, n] = # vtbl + 1; (s)% ⊦ m * (n + 1) = m * n + m; (s)% ⊦ ENCODED_NAT_SIZE ≠ 0; (s)% ⊦ ¬ m + n < m; (s)%# buf ≤ n0, n0 + m ≤ # buf + # buf0 ⊦ subarray(buf + buf0, n0, m) = subarray(buf0, n0 - # buf, m); (s)% ⊦ m + n - m = n; (s)% ⊦ m ≤ m; (s)% ⊦ m - m = 0; (s)% ⊦ n + 0 = n; (s)% ⊦ ¬ n < n; (s)%n + m ≤ # buf ⊦ subarray(buf + buf0, n, m) = subarray(buf, n, m); (s)%# buf = n ⊦ subarray(buf, 0, n) = buf; (s)