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Proof step 2 from proof is-encoded-rec-append (previous step)

# 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, buf) ⊦ is-encoded-rec(vtbl[v, n], buf + buf0), v ∈ vtbl

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
# buf = # vtbl * (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(vtbl, buf) ⊦ is-encoded-rec(vtbl[v, n], buf + 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);% ⊦ # subarray(buf, m, n) = n; (s)%is-encoded-size: ⊦ is-encoded(n, buf) → # buf = ENCODED_NAT_SIZE; (forward) from specification encoding-fixed-size[encoding-nat]%is-encoded-size: ⊦ is-encoded(v, buf) → # buf = ENCODED_VOLID_SIZE; (forward) from specification encoding-fixed-size[encoding-volid]