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Proof step 23 from proof is-encoded-rec-append (previous step)

# buf1 = (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) * m, # vtbl = m + 1, # buf0 = ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE, # buf3 = ENCODED_VOLID_SIZE, # buf2 = ENCODED_NAT_SIZE, is-encoded(n, subarray(buf0, ENCODED_VOLID_SIZE, ENCODED_NAT_SIZE)), is-encoded(v, subarray(buf0, 0, ENCODED_VOLID_SIZE)), is-encoded(vtbl[v0], buf2), is-encoded(v0, buf3), is-encoded-rec(vtbl -- v0, buf1), v0 ∈ vtbl, ∀ vtbl0, buf, buf0, v, n. # vtbl0 < m + 1 → # 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 ⊦ vtbl = ∅, v ∈ vtbl, v0 ∈ vtbl[v, n] ∧ (buf3 + buf2 + buf1) + buf0 = buf3 + buf2 + buf1 + buf0 ∧ is-encoded(v0, buf3) ∧ is-encoded(vtbl[v, n][v0], buf2) ∧ is-encoded-rec(vtbl[v, n] -- v0, buf1 + buf0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 24:
# buf1 = (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) * m, # vtbl = m + 1, # buf0 = ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE, # buf3 = ENCODED_VOLID_SIZE, # buf2 = ENCODED_NAT_SIZE, is-encoded(n, subarray(buf0, ENCODED_VOLID_SIZE, ENCODED_NAT_SIZE)), is-encoded(v, subarray(buf0, 0, ENCODED_VOLID_SIZE)), is-encoded(vtbl[v0], buf2), is-encoded(v0, buf3), is-encoded-rec(vtbl -- v0, buf1), v0 ∈ vtbl, v0 ∈ vtbl[v, n], ∀ vtbl0, buf, buf0, v, n. # vtbl0 < m + 1 → # 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 ⊦ vtbl = ∅, is-encoded-rec(vtbl[v, n] -- v0, buf1 + buf0), v ∈ vtbl

Rule argument

Additional information

Used simplifier rules: ⊦ v ∈ vtbl[v0, n] ↔ v = v0 ∨ v ∈ vtbl; (ws)% ⊦ is-encoded(n, buf) → (is-encoded(n0, buf) ↔ n = n0); (s)% ⊦ v ∈ vtbl ∧ ¬ v0 ∈ vtbl → vtbl[v0, n][v] = vtbl[v]; (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]