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Proof step 75 from proof decode (previous step)

# buf1 = ENCODED_NAT_SIZE, # buf2 = ENCODED_VOLID_SIZE, # vtbl1 = m0 + 1, # buf0 = m0 * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), ENCODED_NAT_SIZE + (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) * # vtbl = # buf4, is-encoded(v, buf2), is-encoded(vtbl1[v], buf1), is-encoded(vtbl0, (buf4 + buf2 + buf1) + buf0 + buf3), is-encoded((m0 + 1) + # vtbl, subarray(buf4, 0, ENCODED_NAT_SIZE)), is-encoded-rec(vtbl1 -- v, buf0), is-encoded-rec(vtbl, subarray(buf4, ENCODED_NAT_SIZE, # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE))), v ∈ vtbl1, # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) ≤ # buf4 + # buf0 + # buf3, ENCODED_NAT_SIZE + (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) * (m0 + # vtbl) ≤ # buf4 + # buf0 + # buf3, vtbl ⊥ vtbl1, err0 = ESUCCESS → n3 = ENCODED_NAT_SIZE, err0 = ESUCCESS ∨ ⌊err0⌋ ⊦ vtbl1 = ∅, is-encoded-rec (vtbl[v, vtbl1[v]], subarray(buf4 + buf2 + buf1, ENCODED_NAT_SIZE, (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) * # vtbl + ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE)), v ∈ vtbl

User applied rule apply lemma

And obtained the following new goals

Proof step 76:
⊦ 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 77:
# buf0 = m0 * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), # vtbl1 = m0 + 1, # buf2 = ENCODED_VOLID_SIZE, # buf1 = ENCODED_NAT_SIZE, ENCODED_NAT_SIZE + (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) * # vtbl = # buf4, is-encoded((m0 + 1) + # vtbl, subarray(buf4, 0, ENCODED_NAT_SIZE)), is-encoded(vtbl0, (buf4 + buf2 + buf1) + buf0 + buf3), is-encoded(vtbl1[v], buf1), is-encoded(v, buf2), is-encoded-rec(vtbl, subarray(buf4, ENCODED_NAT_SIZE, # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE))), is-encoded-rec(vtbl1 -- v, buf0), v ∈ vtbl1, ENCODED_NAT_SIZE + (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) * (m0 + # vtbl) ≤ # buf4 + # buf0 + # buf3, # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) ≤ # buf4 + # buf0 + # buf3, vtbl ⊥ vtbl1, err0 = ESUCCESS → n3 = ENCODED_NAT_SIZE, is-encoded-rec(vtbl, subarray(buf4, ENCODED_NAT_SIZE, (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) * # vtbl)) ∧ ¬ v ∈ vtbl ∧ #(buf2 + buf1) = ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE ∧ is-encoded(v, subarray(buf2 + buf1, 0, ENCODED_VOLID_SIZE)) ∧ is-encoded(vtbl1[v], subarray(buf2 + buf1, ENCODED_VOLID_SIZE, ENCODED_NAT_SIZE)) → is-encoded-rec(vtbl[v, vtbl1[v]], subarray(buf4, ENCODED_NAT_SIZE, (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) * # vtbl) + buf2 + buf1), err0 = ESUCCESS ∨ ⌊err0⌋ ⊦ vtbl1 = ∅, is-encoded-rec (vtbl[v, vtbl1[v]], subarray(buf4 + buf2 + buf1, ENCODED_NAT_SIZE, (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) * # vtbl + ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE)), v ∈ vtbl

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: [vtbl, buf, v, buf0, n] → [vtbl, subarray (buf4, ENCODED_NAT_SIZE, (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) * # vtbl), v, buf2 + buf1, vtbl1[v]]

Additional information

Used terms: vtbl, subarray (buf4, ENCODED_NAT_SIZE, (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) * # vtbl), v, buf2 + buf1, vtbl1[v]