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Proof step 17 from proof is-encoded-rec-unique (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 18:
# buf2 = ENCODED_VOLID_SIZE, # buf1 = ENCODED_NAT_SIZE, # buf0 = # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE + # buf0 = # vtbl1 * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), # vtbl + 1 = # vtbl1, is-encoded(vtbl[v, n][v0], buf1), is-encoded(v0, buf2), is-encoded-rec(vtbl1, buf2 + buf1 + buf0), is-encoded-rec(vtbl[v, n] -- v0, buf0), 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, 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);% ⊦ ENCODED_VOLID_SIZE ≠ 0; (s)% ⊦ m + n = 0 ↔ m = 0 ∧ n = 0; (ws)%mult-c: ⊦ m * n = n * m; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult% ⊦ m * n + n = m1 * n ↔ m + 1 = m1 ∨ n = 0; (s)%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)% ⊦ 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]% ⊦ vtbl[v, n] ≠ ∅; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[encoding-nat-buffer]% ⊦ #(buf + buf0) = # buf + # buf0; (s)