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Proof step 11 from proof is-encoded-rec-append (previous step)

# buf = 0, # 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)), ∀ 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 ⊦ v ∈ (∅)[v, n] ∧ buf0 = subarray(buf0, 0, ENCODED_VOLID_SIZE) + subarray(buf0, ENCODED_VOLID_SIZE, ENCODED_NAT_SIZE) + mkbuf(0) ∧ is-encoded(v, subarray(buf0, 0, ENCODED_VOLID_SIZE)) ∧ is-encoded((∅)[v, n][v], subarray(buf0, ENCODED_VOLID_SIZE, ENCODED_NAT_SIZE)) ∧ is-encoded-rec((∅)[v, n] -- v, mkbuf(0))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
# 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 ⊦ buf0 = subarray(buf0, 0, ENCODED_VOLID_SIZE) + subarray(buf0, ENCODED_VOLID_SIZE, ENCODED_NAT_SIZE)

Rule argument

Additional information

Used simplifier rules: is-encoded-base: ⊦ is-encoded-rec(∅, buf) ↔ # buf = 0;% ⊦ # mkbuf(n) = n; (s)% ⊦ ∅ -- v = ∅; (s)% ⊦ vtbl[v, n] -- v = vtbl -- v; (s)% ⊦ is-encoded(n, buf) → (is-encoded(n0, buf) ↔ n = n0); (s)% ⊦ vtbl[v, n][v] = n; (s)% ⊦ is-encoded(v, buf) → (is-encoded(v0, buf) ↔ v = v0); (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[encoding-nat-buffer]% ⊦ buf + mkbuf(0) = buf; (s)% ⊦ v ∈ vtbl[v, n]; (s)