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Proof step 85 from proof encode (previous step)

# buf4 = 2 * ENCODED_NAT_SIZE + n0 + # buf2 + ENCODED_VOLID_SIZE, # buf11 = 0, # buf7 = ENCODED_NAT_SIZE, # vtbl1 = m + 1, # buf1 = 0, # buf = 0, # buf8 = ENCODED_VOLID_SIZE, # buf0 = ENCODED_NAT_SIZE, # buf2 = # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), # buf3 = 0, # buf10 = 0, ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE + n0 = # buf9, ENCODED_NAT_SIZE + # buf2 + # buf9 = # buf4, ENCODED_NAT_SIZE = # buf5, is-encoded(#(vtbl1 ∪ vtbl), buf0), is-encoded(v, subarray(buf9, 0, ENCODED_VOLID_SIZE)), is-encoded(vtbl1[v], subarray(buf9, ENCODED_VOLID_SIZE, ENCODED_NAT_SIZE)), is-encoded-rec(vtbl, buf2), v ∈ vtbl1, #(vtbl1 ∪ vtbl) * (ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE) ≤ # buf2 + # buf9, (ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE) * m ≤ n0, 2 * ENCODED_NAT_SIZE + # buf2 + ENCODED_VOLID_SIZE ≤ # buf4, ENCODED_NAT_SIZE + # buf2 + ENCODED_VOLID_SIZE ≤ # buf4, ENCODED_VOLID_SIZE ≤ # buf9, vtbl1 ⊥ vtbl, err0 = ESUCCESS → is-encoded(#(vtbl1 ∪ vtbl), subarray(buf4, 0, ENCODED_NAT_SIZE)) ∧ n1 = ENCODED_NAT_SIZE, err0 = ESUCCESS ∨ ⌊err0⌋ ⊦ vtbl1 = ∅, v ∈ vtbl, buf0 + buf2 + buf9 = buf0 + (buf2 + subarray(buf9, 0, ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE)) + subarray(buf9, ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE, # buf9 - ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE) ∧ vtbl1 ∪ vtbl = (vtbl1 -- v) ∪ vtbl[v, vtbl1[v]] ∧ vtbl1 -- v ⊥ vtbl[v, vtbl1[v]] ∧ # buf0 + #(buf2 + subarray(buf9, 0, ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE)) = 2 * ENCODED_NAT_SIZE + # buf2 + ENCODED_VOLID_SIZE ∧ m * (ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE) ≤ # subarray(buf9, ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE, # buf9 - ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE) ∧ is-encoded(#((vtbl1 -- v) ∪ vtbl[v, vtbl1[v]]), buf0) ∧ is-encoded-rec(vtbl[v, vtbl1[v]], buf2 + subarray(buf9, 0, ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: is-encoded-rec-size: ⊦ is-encoded-rec(vtbl, buf) → # buf = # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE);% ⊦ m ≤ n → (n < m ↔ false); (s)%n0 ≤ n ⊦ m ≤ n - n0 ↔ m + n0 ≤ n; (s)% ⊦ ¬ m + n < m; (s)% ⊦ m + n < m + n0 ↔ n < n0; (s)% ⊦ m < n → n ≠ 0; (s)% ⊦ m * (n + 1) = m * n + m; (s)% ⊦ ¬ v ∈ vtbl → # vtbl[v, n] = # vtbl + 1; (s)%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ is-encoded(n, buf) → (is-encoded(n0, buf) ↔ n = n0); (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)%c: ⊦ m + n = n + m; 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 = m + n0 ↔ (m2 - 1) * m = n0; (s)% ⊦ m + n = m + n0 ↔ n = n0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ # subarray(buf, m, n) = n; (s)% ⊦ #(buf + buf0) = # buf + # buf0; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[encoding-nat-buffer]% ⊦ buf + buf0 = buf + buf1 ↔ buf0 = buf1; (s)