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Proof step 20 from proof is-encoded-rec-unique (previous step)

# buf0 = # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), # buf1 = ENCODED_NAT_SIZE, # buf2 = ENCODED_VOLID_SIZE, # vtbl + 1 = # vtbl1, ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE + # buf0 = # vtbl1 * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), is-encoded(v0, buf2), is-encoded(vtbl[v, n][v0], buf1), is-encoded-rec(vtbl[v, n] -- v0, buf0), v0 ∈ vtbl[v, n], ∃ v, buf5, buf4, buf3. v ∈ vtbl1 ∧ buf2 + buf1 + buf0 = buf5 + buf4 + buf3 ∧ is-encoded(v, buf5) ∧ is-encoded(vtbl1[v], buf4) ∧ is-encoded-rec(vtbl1 -- v, buf3), ∀ 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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 21:
# 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 = (# vtbl1 - 1) * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), # vtbl + 1 = # vtbl1, ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE + # buf0 = # vtbl1 * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), 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

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]