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Proof step 50 from proof encode (previous step)

# buf3 = ENCODED_VOLID_SIZE + n2, # buf = # buf4, # buf4 = (# buf2 + ENCODED_VOLID_SIZE + n2) + ENCODED_NAT_SIZE, # buf0 = ENCODED_NAT_SIZE, # buf2 = # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), # buf5 = # buf4, subarray(buf4, ENCODED_NAT_SIZE, # buf2 + ENCODED_VOLID_SIZE + n2) = subarray(buf, ENCODED_NAT_SIZE, # buf2 + ENCODED_VOLID_SIZE + n2), subarray(buf5, ENCODED_NAT_SIZE + # buf2 + ENCODED_VOLID_SIZE, n2) = subarray(buf3, ENCODED_VOLID_SIZE, n2), subarray(buf5, 0, ENCODED_NAT_SIZE + # buf2) = buf0 + buf2, # buf4 < 2 * ENCODED_NAT_SIZE + # buf2 + ENCODED_VOLID_SIZE, n2 < ENCODED_NAT_SIZE, is-encoded(#(vtbl1 ∪ vtbl), buf0), is-encoded(v, subarray(buf5, ENCODED_NAT_SIZE + # buf2, ENCODED_VOLID_SIZE)), is-encoded-rec(vtbl, buf2), v ∈ vtbl1, #(vtbl1 ∪ vtbl) * (ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE) ≤ # buf2 + ENCODED_VOLID_SIZE + n2, # vtbl1 * (ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE) ≤ ENCODED_VOLID_SIZE + n2, ENCODED_NAT_SIZE + # buf2 + ENCODED_VOLID_SIZE ≤ # buf4, 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]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 51:
# buf5 = # buf4, # buf2 = # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), # buf0 = ENCODED_NAT_SIZE, # buf4 = (# buf2 + ENCODED_VOLID_SIZE + n2) + ENCODED_NAT_SIZE, # buf = # buf4, # buf3 = ENCODED_VOLID_SIZE + n2, subarray(buf5, 0, ENCODED_NAT_SIZE + # buf2) = buf0 + buf2, subarray(buf5, ENCODED_NAT_SIZE + # buf2 + ENCODED_VOLID_SIZE, n2) = subarray(buf3, ENCODED_VOLID_SIZE, n2), subarray(buf4, ENCODED_NAT_SIZE, # buf2 + ENCODED_VOLID_SIZE + n2) = subarray(buf, ENCODED_NAT_SIZE, # buf2 + ENCODED_VOLID_SIZE + n2), n2 < ENCODED_NAT_SIZE, # buf4 < 2 * ENCODED_NAT_SIZE + # buf2 + ENCODED_VOLID_SIZE, is-encoded(v, subarray(buf5, ENCODED_NAT_SIZE + # buf2, ENCODED_VOLID_SIZE)), is-encoded(#(vtbl1 ∪ vtbl), buf0), is-encoded-rec(vtbl, buf2), v ∈ vtbl1, v0 ∈ vtbl1, ENCODED_NAT_SIZE + # buf2 + ENCODED_VOLID_SIZE ≤ # buf4, # vtbl1 * (ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE) ≤ ENCODED_VOLID_SIZE + n2, #(vtbl1 ∪ vtbl) * (ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE) ≤ # buf2 + ENCODED_VOLID_SIZE + n2, vtbl1 ⊥ vtbl, err0 = ESUCCESS → is-encoded(#(vtbl1 ∪ vtbl), subarray(buf4, 0, ENCODED_NAT_SIZE)) ∧ n1 = ENCODED_NAT_SIZE, err0 = ESUCCESS ∨ ⌊err0⌋ ⊦ v ∈ vtbl, v0 ∈ vtbl

Rule argument

Additional information

Used simplifier rules: disjoint-in-left: ⊦ v ∈ vtbl ∧ vtbl ⊥ vtbl0 → ¬ v ∈ vtbl0; (forward) from specification store-union[vtbl]% ⊦ ¬ v ∈ vtbl → vtbl[v] = (∅)[v]; (s)% ⊦ ¬ v ∈ ∅; (s)