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Proof step 30 from proof encode (previous step)

# buf = # buf4, # buf4 = (# buf2 + # buf3) + ENCODED_NAT_SIZE, # buf0 = ENCODED_NAT_SIZE, # buf2 = # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), subarray(buf4, ENCODED_NAT_SIZE, # buf2 + # buf3) = subarray(buf, ENCODED_NAT_SIZE, # buf2 + # buf3), # vtbl1 * (ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE) < ENCODED_VOLID_SIZE, # buf3 < ENCODED_VOLID_SIZE, is-encoded(#(vtbl1 ∪ vtbl), buf0), is-encoded-rec(vtbl, buf2), v ∈ vtbl1, #(vtbl1 ∪ vtbl) * (ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE) ≤ # buf2 + # buf3, # vtbl1 * (ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE) ≤ # buf3, vtbl1 ⊥ vtbl, err0 = ESUCCESS → is-encoded(#(vtbl1 ∪ vtbl), subarray(buf4, 0, ENCODED_NAT_SIZE)) ∧ n1 = ENCODED_NAT_SIZE, err0 = ESUCCESS ∨ ⌊err0⌋ ⊦ vtbl1 = ∅, v ∈ vtbl

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 31:
⊦ vtbl = vtbl0 ↔ (∀ v. (v ∈ vtbl ↔ v ∈ vtbl0) ∧ vtbl[v] = vtbl0[v])
Proof step 32:
# buf2 = # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), # buf0 = ENCODED_NAT_SIZE, # buf4 = (# buf2 + # buf3) + ENCODED_NAT_SIZE, # buf = # buf4, subarray(buf4, ENCODED_NAT_SIZE, # buf2 + # buf3) = subarray(buf, ENCODED_NAT_SIZE, # buf2 + # buf3), # buf3 < ENCODED_VOLID_SIZE, # vtbl1 * (ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE) < ENCODED_VOLID_SIZE, is-encoded(#(vtbl1 ∪ vtbl), buf0), is-encoded-rec(vtbl, buf2), v ∈ vtbl1, # vtbl1 * (ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE) ≤ # buf3, #(vtbl1 ∪ vtbl) * (ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE) ≤ # buf2 + # buf3, vtbl1 ⊥ vtbl, err0 = ESUCCESS → is-encoded(#(vtbl1 ∪ vtbl), subarray(buf4, 0, ENCODED_NAT_SIZE)) ∧ n1 = ENCODED_NAT_SIZE, err0 = ESUCCESS ∨ ⌊err0⌋ ⊦ v ∈ vtbl, ∀ v. (v ∈ vtbl1 ↔ v ∈ ∅) ∧ vtbl1[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] → [∅, vtbl1] flags: <all paths>

Additional information

Used terms: ∅, vtbl1