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Proof step 16 from proof is-encoded-rec-append (previous step)

# buf0 = ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE, # buf = # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), is-encoded(n, subarray(buf0, ENCODED_VOLID_SIZE, ENCODED_NAT_SIZE)), is-encoded(v, subarray(buf0, 0, ENCODED_VOLID_SIZE)), ∃ 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), ∀ 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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 17:
# buf0 = ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE, # buf3 = ENCODED_VOLID_SIZE, # buf2 = ENCODED_NAT_SIZE, # buf1 = (# vtbl - 1) * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE + # buf1 = # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), is-encoded(n, subarray(buf0, ENCODED_VOLID_SIZE, ENCODED_NAT_SIZE)), is-encoded(v, subarray(buf0, 0, ENCODED_VOLID_SIZE)), is-encoded(vtbl[v0], buf2), is-encoded(v0, buf3), is-encoded-rec(vtbl -- v0, buf1), v0 ∈ vtbl, ∀ 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], (buf3 + buf2 + buf1) + buf0), v ∈ vtbl

Rule argument

Additional information

Used simplifier rules: is-encoded-rec-size: ⊦ is-encoded-rec(vtbl, buf) → # buf = # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE);% ⊦ n -1 = n - 1; (s)% ⊦ v ∈ vtbl → #(vtbl -- v) = (# vtbl)-1; (s)%is-encoded-size: ⊦ is-encoded(v, buf) → # buf = ENCODED_VOLID_SIZE; (forward) from specification encoding-fixed-size[encoding-volid]%is-encoded-size: ⊦ is-encoded(n, buf) → # buf = ENCODED_NAT_SIZE; (forward) from specification encoding-fixed-size[encoding-nat]%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[encoding-nat-buffer]% ⊦ #(buf + buf0) = # buf + # buf0; (s)