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Proof step 9 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, n] = ∅, ∃ v0, buf3, buf1, buf2. v0 ∈ (∅)[v, n] ∧ buf0 = buf3 + buf1 + buf2 ∧ is-encoded(v0, buf3) ∧ is-encoded((∅)[v, n][v0], buf1) ∧ is-encoded-rec((∅)[v, n] -- v0, buf2)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
# 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 ⊦ ∃ v0, buf3, buf1, buf2. v0 ∈ (∅)[v, n] ∧ buf0 = buf3 + buf1 + buf2 ∧ is-encoded(v0, buf3) ∧ is-encoded((∅)[v, n][v0], buf1) ∧ is-encoded-rec((∅)[v, n] -- v0, buf2)

Rule argument

Additional information

Used simplifier rules: ⊦ vtbl[v, n] ≠ ∅; (s)