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

# vtbl1 = # vtbl + 1, # buf0 = # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), # buf1 = ENCODED_NAT_SIZE, # buf2 = ENCODED_VOLID_SIZE, # buf4 = ENCODED_VOLID_SIZE, # buf3 = ENCODED_NAT_SIZE, # buf = # buf0, buf2 + buf1 + buf0 = buf4 + buf3 + buf, is-encoded(v0, buf2), is-encoded(vtbl[v, n][v0], buf1), is-encoded(vtbl1[v1], buf3), is-encoded(v1, buf4), is-encoded-rec(vtbl[v, n] -- v0, buf0), is-encoded-rec(vtbl1 -- v1, buf), v0 ∈ vtbl[v, n], v1 ∈ vtbl1, ∀ vtbl2, buf, vtbl1. # vtbl2 < # vtbl[v, n] → # buf = # vtbl1 * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) ∧ # buf = # vtbl2 * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) ∧ is-encoded-rec(vtbl2, buf) ∧ is-encoded-rec(vtbl1, buf) → vtbl2 = vtbl1 ⊦ ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE = 0, vtbl[v, n] = vtbl1, vtbl1 = ∅, v ∈ vtbl

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 24:
⊦ # buf = # buf0 → (buf + buf1 = buf0 + buf2 ↔ buf = buf0 ∧ buf1 = buf2)
Proof step 25:
# buf = # buf0, # buf3 = ENCODED_NAT_SIZE, # buf4 = ENCODED_VOLID_SIZE, # buf2 = ENCODED_VOLID_SIZE, # buf1 = ENCODED_NAT_SIZE, # buf0 = # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), # vtbl1 = # vtbl + 1, # buf2 = # buf4, buf1 + buf0 = buf3 + buf, buf2 = buf4, is-encoded(v1, buf4), is-encoded(vtbl1[v1], buf3), is-encoded(vtbl[v, n][v0], buf1), is-encoded(v0, buf2), is-encoded-rec(vtbl1 -- v1, buf), is-encoded-rec(vtbl[v, n] -- v0, buf0), v1 ∈ vtbl1, v0 ∈ vtbl[v, n], ∀ vtbl2, buf, vtbl1. # vtbl2 < # vtbl[v, n] → # buf = # vtbl1 * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) ∧ # buf = # vtbl2 * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) ∧ is-encoded-rec(vtbl2, buf) ∧ is-encoded-rec(vtbl1, buf) → vtbl2 = vtbl1 ⊦ ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE = 0, vtbl[v, n] = vtbl1, vtbl1 = ∅, v ∈ vtbl

Rule argument

spec: array-splice, inst: encoding-nat-buffer name: append-inj seq: ⊦ # buf = # buf0 → (buf + buf1 = buf0 + buf2 ↔ buf = buf0 ∧ buf1 = buf2) subst: [buf2, buf0, buf1, buf] → [buf3 + buf, buf4, buf1 + buf0, buf2] flags: <all paths>

Additional information

Used terms: buf3 + buf, buf4, buf1 + buf0, buf2