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Proof step 89 from proof encode (previous step)

# buf4 = 2 * ENCODED_NAT_SIZE + n0 + # buf2 + ENCODED_VOLID_SIZE, # buf11 = 0, # buf7 = ENCODED_NAT_SIZE, # vtbl1 = m + 1, # buf1 = 0, # buf = 0, # buf8 = ENCODED_VOLID_SIZE, # buf0 = ENCODED_NAT_SIZE, # buf2 = # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), # buf3 = 0, # buf10 = 0, ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE + n0 = # buf9, ENCODED_NAT_SIZE + # buf2 + # buf9 = # buf4, ENCODED_NAT_SIZE = # buf5, is-encoded(#(vtbl1 ∪ vtbl), buf0), is-encoded(v, subarray(buf9, 0, ENCODED_VOLID_SIZE)), is-encoded(vtbl1[v], subarray(buf9, ENCODED_VOLID_SIZE, ENCODED_NAT_SIZE)), is-encoded-rec(vtbl, buf2), v ∈ vtbl1, ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE ≤ # buf9, #(vtbl1 ∪ vtbl) * (ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE) ≤ # buf2 + # buf9, (ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE) * m ≤ n0, 2 * ENCODED_NAT_SIZE + # buf2 + ENCODED_VOLID_SIZE ≤ # buf4, ENCODED_NAT_SIZE + # buf2 + ENCODED_VOLID_SIZE ≤ # buf4, ENCODED_VOLID_SIZE ≤ # buf9, m * (ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE) + ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE ≤ # buf9, vtbl1 ⊥ vtbl, err0 = ESUCCESS → is-encoded(#(vtbl1 ∪ vtbl), subarray(buf4, 0, ENCODED_NAT_SIZE)) ∧ n1 = ENCODED_NAT_SIZE, err0 = ESUCCESS ∨ ⌊err0⌋ ⊦ vtbl1 = ∅, is-encoded-rec(vtbl[v, vtbl1[v]], buf2 + subarray(buf9, 0, ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE)), v ∈ vtbl

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 90:
⊦ is-encoded-rec(vtbl, buf) ∧ ¬ v ∈ vtbl ∧ # 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[v, n], buf + buf0)
Proof step 91:
# buf10 = 0, # buf3 = 0, # buf2 = # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), # buf0 = ENCODED_NAT_SIZE, # buf8 = ENCODED_VOLID_SIZE, # buf = 0, # buf1 = 0, # vtbl1 = m + 1, # buf7 = ENCODED_NAT_SIZE, # buf11 = 0, # buf4 = 2 * ENCODED_NAT_SIZE + n0 + # buf2 + ENCODED_VOLID_SIZE, ENCODED_NAT_SIZE + # buf2 + # buf9 = # buf4, ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE + n0 = # buf9, ENCODED_NAT_SIZE = # buf5, is-encoded(vtbl1[v], subarray(buf9, ENCODED_VOLID_SIZE, ENCODED_NAT_SIZE)), is-encoded(v, subarray(buf9, 0, ENCODED_VOLID_SIZE)), is-encoded(#(vtbl1 ∪ vtbl), buf0), is-encoded-rec(vtbl, buf2), v ∈ vtbl1, m * (ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE) + ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE ≤ # buf9, ENCODED_VOLID_SIZE ≤ # buf9, ENCODED_NAT_SIZE + # buf2 + ENCODED_VOLID_SIZE ≤ # buf4, 2 * ENCODED_NAT_SIZE + # buf2 + ENCODED_VOLID_SIZE ≤ # buf4, (ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE) * m ≤ n0, #(vtbl1 ∪ vtbl) * (ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE) ≤ # buf2 + # buf9, ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE ≤ # buf9, vtbl1 ⊥ vtbl, err0 = ESUCCESS → is-encoded(#(vtbl1 ∪ vtbl), subarray(buf4, 0, ENCODED_NAT_SIZE)) ∧ n1 = ENCODED_NAT_SIZE, err0 = ESUCCESS ∨ ⌊err0⌋ ⊦ vtbl1 = ∅, is-encoded-rec(vtbl[v, vtbl1[v]], buf2 + subarray(buf9, 0, ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE)), v ∈ vtbl, is-encoded-rec(vtbl, buf2) ∧ ¬ v ∈ vtbl ∧ # subarray(buf9, 0, ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE) = ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE ∧ is-encoded(v, subarray(subarray(buf9, 0, ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE), 0, ENCODED_VOLID_SIZE)) ∧ is-encoded(vtbl1[v], subarray(subarray(buf9, 0, ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE), ENCODED_VOLID_SIZE, ENCODED_NAT_SIZE))

Rule argument

spec: <toplevel> name: is-encoded-rec-append seq: ⊦ is-encoded-rec(vtbl, buf) ∧ ¬ v ∈ vtbl ∧ # 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[v, n], buf + buf0) subst: [buf0, buf, n, v, vtbl] → [subarray(buf9, 0, ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE), buf2, vtbl1[v], v, vtbl] flags: <all paths>

Additional information

Used terms: subarray(buf9, 0, ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE), buf2, vtbl1[v], v, vtbl