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Proof step 12 from proof is-encoded-rec-unique (previous step)

# buf = # vtbl1 * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), # buf = # vtbl0 * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), is-encoded-rec(vtbl0, buf), is-encoded-rec(vtbl1, 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

User applied rule apply lemma

And obtained the following new goals

Proof step 13:
⊦ v ∈ vtbl ↔ (∃ n, vtbl0. vtbl = vtbl0[v, n] ∧ ¬ v ∈ vtbl0)
Proof step 14:
# 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

Rule argument

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

Additional information

Used terms: v, vtbl0