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Proof step 8 from proof is-encoded-rec-size (previous step)

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)

User applied rule apply lemma

And obtained the following new goals

Proof step 9:
⊦ v ∈ vtbl ↔ (∃ n, vtbl0. vtbl = vtbl0[v, n] ∧ ¬ v ∈ vtbl0)
Proof step 10:
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)

Rule argument

spec: store, inst: vtbl name: exin seq: ⊦ v ∈ vtbl ↔ (∃ n, vtbl0. vtbl = vtbl0[v, n] ∧ ¬ v ∈ vtbl0) subst: [v, vtbl] → [v, vtbl]

Additional information

Used terms: v, vtbl