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Proof step 10 from proof is-encoded-rec-size (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 11:
is-encoded-rec(vtbl0[v, n], buf), ∀ vtbl1, buf. # vtbl1 < # vtbl0[v, n] → is-encoded-rec(vtbl1, buf) → # buf = # vtbl1 * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) ⊦ # buf = (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) * # vtbl0 + ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE, v ∈ vtbl0

Rule argument

Additional information

Used simplifier rules: 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)