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Proof step 22 from proof is-encoded-rec-append (previous step)

# buf2 = ENCODED_NAT_SIZE, # buf3 = ENCODED_VOLID_SIZE, # buf0 = ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE, # vtbl = m + 1, # buf1 = (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) * m, is-encoded(v0, buf3), is-encoded(vtbl[v0], buf2), is-encoded(v, subarray(buf0, 0, ENCODED_VOLID_SIZE)), is-encoded(n, subarray(buf0, ENCODED_VOLID_SIZE, ENCODED_NAT_SIZE)), 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, buf6, buf5, buf4. v0 ∈ vtbl[v, n] ∧ (buf3 + buf2 + buf1) + buf0 = buf6 + buf5 + buf4 ∧ is-encoded(v0, buf6) ∧ is-encoded(vtbl[v, n][v0], buf5) ∧ is-encoded-rec(vtbl[v, n] -- v0, buf4)

User applied rule exists right

And obtained the following new goals

Proof step 23:
# 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)

Rule argument

pos: right 3 terms: v0, buf3, buf2, buf1 + buf0 abort: F discard: T computed: F

Additional information

Used terms: v0, buf3, buf2, buf1 + buf0