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Proof step 6 from proof is-encoded-unique (previous step)

# buf1 = # vtbl0 * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), # buf2 = ENCODED_NAT_SIZE, is-encoded(# vtbl0, buf2), is-encoded(vtbl1, buf2 + buf1 + buf0), is-encoded-rec(vtbl0, buf1) ⊦ vtbl0 = vtbl1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ is-encoded(vtbl, buf) ↔ (∃ buf0, buf1, buf2. buf = buf0 + buf1 + buf2 ∧ is-encoded(# vtbl, buf0) ∧ is-encoded-rec(vtbl, buf1))
Proof step 8:
# buf2 = ENCODED_NAT_SIZE, # buf1 = # vtbl0 * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), is-encoded(# vtbl0, buf2), is-encoded-rec(vtbl0, buf1), ∃ buf5, buf4, buf3. buf2 + buf1 + buf0 = buf5 + buf4 + buf3 ∧ is-encoded(# vtbl1, buf5) ∧ is-encoded-rec(vtbl1, buf4) ⊦ vtbl0 = vtbl1

Rule argument

spec: <toplevel> name: is-encoded seq: ⊦ is-encoded(vtbl, buf) ↔ (∃ buf0, buf1, buf2. buf = buf0 + buf1 + buf2 ∧ is-encoded(# vtbl, buf0) ∧ is-encoded-rec(vtbl, buf1)) subst: [buf, vtbl] → [buf2 + buf1 + buf0, vtbl1] flags: <all paths>

Additional information

Used terms: buf2 + buf1 + buf0, vtbl1