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Proof step 14 from proof is-encoded-rec-append (previous step)

# buf = # vtbl * (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(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 ⊦ vtbl = ∅, is-encoded-rec(vtbl[v, n], buf + buf0), v ∈ vtbl

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: is-encoded-rec seq: vtbl ≠ ∅ ⊦ is-encoded-rec(vtbl, buf) ↔ (∃ v, buf0, buf1, buf2. v ∈ vtbl ∧ buf = buf0 + buf1 + buf2 ∧ is-encoded(v, buf0) ∧ is-encoded(vtbl[v], buf1) ∧ is-encoded-rec(vtbl -- v, buf2)) subst: [buf, vtbl] → [buf, vtbl] flags: <all paths>

Additional information

Used terms: buf, vtbl