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Proof step 6 from proof is-encoded-rec-append (previous step)

# buf = # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), # buf0 = ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE, vtbl = ∅, is-encoded(v, subarray(buf0, 0, ENCODED_VOLID_SIZE)), is-encoded(n, subarray(buf0, ENCODED_VOLID_SIZE, ENCODED_NAT_SIZE)), is-encoded-rec(vtbl, buf), ∀ vtbl0, buf, buf0, v, n. # vtbl0 < # vtbl → # buf = # vtbl0 * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) ∧ # buf0 = ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE ∧ is-encoded(v, subarray(buf0, 0, ENCODED_VOLID_SIZE)) ∧ is-encoded(n, subarray(buf0, ENCODED_VOLID_SIZE, ENCODED_NAT_SIZE)) ∧ is-encoded-rec(vtbl0, buf) → is-encoded-rec(vtbl0[v, n], buf + buf0) ∨ v ∈ vtbl0 ⊦ is-encoded-rec(vtbl[v, n], buf + buf0), v ∈ vtbl

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
# buf0 = ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE, # buf = 0, is-encoded(n, subarray(buf0, ENCODED_VOLID_SIZE, ENCODED_NAT_SIZE)), is-encoded(v, subarray(buf0, 0, ENCODED_VOLID_SIZE)), ∀ vtbl0, buf, buf0, v, n. # vtbl0 < # ∅ → # buf = # vtbl0 * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) ∧ # buf0 = ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE ∧ is-encoded(v, subarray(buf0, 0, ENCODED_VOLID_SIZE)) ∧ is-encoded(n, subarray(buf0, ENCODED_VOLID_SIZE, ENCODED_NAT_SIZE)) ∧ is-encoded-rec(vtbl0, buf) → is-encoded-rec(vtbl0[v, n], buf + buf0) ∨ v ∈ vtbl0 ⊦ is-encoded-rec((∅)[v, n], buf0)

Rule argument

Additional information

Used simplifier rules: is-encoded-base: ⊦ is-encoded-rec(∅, buf) ↔ # buf = 0;%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[encoding-nat-buffer]% ⊦ # buf = 0 → buf + buf0 = buf0; (s)% ⊦ ¬ v ∈ ∅; (s)%mult-c: ⊦ m * n = n * m; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult% ⊦ 0 * n = 0; (s)% ⊦ # ∅ = 0; (s)