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Proof step 25 from proof is-encoded-rec-unique (previous step)

# buf = # buf0, # buf3 = ENCODED_NAT_SIZE, # buf4 = ENCODED_VOLID_SIZE, # buf2 = ENCODED_VOLID_SIZE, # buf1 = ENCODED_NAT_SIZE, # buf0 = # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), # vtbl1 = # vtbl + 1, # buf2 = # buf4, buf1 + buf0 = buf3 + buf, buf2 = buf4, is-encoded(v1, buf4), is-encoded(vtbl1[v1], buf3), is-encoded(vtbl[v, n][v0], buf1), is-encoded(v0, buf2), is-encoded-rec(vtbl1 -- v1, buf), is-encoded-rec(vtbl[v, n] -- v0, buf0), v1 ∈ vtbl1, v0 ∈ vtbl[v, n], ∀ 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 26:
# vtbl1 = # vtbl + 1, # buf = # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), # buf4 = ENCODED_VOLID_SIZE, # buf3 = ENCODED_NAT_SIZE, # buf = (# vtbl1 - 1) * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), vtbl1[v0] = vtbl[v, n][v0], is-encoded(vtbl1[v0], buf3), is-encoded(v0, buf4), is-encoded-rec(vtbl[v, n] -- v0, buf), is-encoded-rec(vtbl1 -- v0, buf), v0 ∈ vtbl[v, n], v0 ∈ 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);%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ (m + 1)-1 = m; (s)% ⊦ ¬ v ∈ vtbl → # vtbl[v, n] = # vtbl + 1; (s)% ⊦ n -1 = n - 1; (s)% ⊦ v ∈ vtbl → #(vtbl -- v) = (# vtbl)-1; (s)%⊦ # buf = # buf0 → (buf + buf1 = buf0 + buf2 ↔ buf = buf0 ∧ buf1 = buf2); (ws)%⊦ buf0 + buf1 = buf2 + buf3 ∧ is-encoded(n, buf0) → (is-encoded(n0, buf2) ↔ # buf0 = # buf2 ∧ n = n0); (ws)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[encoding-nat-buffer]% ⊦ is-encoded(v, buf) → (is-encoded(v0, buf) ↔ v = v0); (s)