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Proof step 14 from proof is-encoded-rec-unique (previous step)

# buf = # vtbl0 * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), # buf = # vtbl1 * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), v ∈ vtbl0 ↔ (∃ n, vtbl1. vtbl0 = vtbl1[v, n] ∧ ¬ v ∈ vtbl1), is-encoded-rec(vtbl1, buf), is-encoded-rec(vtbl0, buf), v ∈ vtbl0, ∀ vtbl, buf, vtbl1. # vtbl < # vtbl0 → # buf = # vtbl1 * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) ∧ # buf = # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) ∧ is-encoded-rec(vtbl, buf) ∧ is-encoded-rec(vtbl1, buf) → vtbl = vtbl1 ⊦ vtbl0 = vtbl1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
# buf = (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) * # vtbl + ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE, # buf = # vtbl1 * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), is-encoded-rec(vtbl[v, n], buf), is-encoded-rec(vtbl1, buf), ∀ 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, 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);%mult-c: ⊦ m * n = n * m; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m * (n + 1) = m * n + m; (s)% ⊦ ¬ v ∈ vtbl → # vtbl[v, n] = # vtbl + 1; (s)% ⊦ v ∈ vtbl[v0, n] ↔ v = v0 ∨ v ∈ vtbl; (ws)