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Proof step 5 from proof is-encoded-rec-size (previous step)

is-encoded-rec(vtbl, buf), ∀ 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), vtbl = ∅

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ vtbl = vtbl0 ↔ (∀ v. (v ∈ vtbl ↔ v ∈ vtbl0) ∧ vtbl[v] = vtbl0[v])
Proof step 7:
is-encoded-rec(vtbl, buf), ∀ 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), ∀ v. (v ∈ vtbl ↔ v ∈ ∅) ∧ vtbl[v] = (∅)[v]

Rule argument

spec: store, inst: vtbl name: Extension seq: ⊦ vtbl = vtbl0 ↔ (∀ v. (v ∈ vtbl ↔ v ∈ vtbl0) ∧ vtbl[v] = vtbl0[v]) subst: [vtbl0, vtbl] → [∅, vtbl] flags: <all paths>

Additional information

Used terms: ∅, vtbl