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Proof step 128 from proof encode (previous step)

# buf4 = 2 * ENCODED_NAT_SIZE + n0 + # buf2 + ENCODED_VOLID_SIZE, # buf11 = 0, # buf7 = ENCODED_NAT_SIZE, # vtbl1 = m + 1, # buf1 = 0, # buf = 0, # buf8 = ENCODED_VOLID_SIZE, # buf0 = ENCODED_NAT_SIZE, # buf2 = # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), # buf3 = 0, # buf10 = 0, ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE + n0 = # buf9, ENCODED_NAT_SIZE + # buf2 + # buf9 = # buf4, ENCODED_NAT_SIZE = # buf5, is-encoded(#(vtbl1 ∪ vtbl), buf0), is-encoded(v, subarray(buf9, 0, ENCODED_VOLID_SIZE)), is-encoded(vtbl1[v], subarray(buf9, ENCODED_VOLID_SIZE, ENCODED_NAT_SIZE)), is-encoded-rec(vtbl, buf2), v ∈ vtbl1, ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE ≤ # buf9, #(vtbl1 ∪ vtbl) * (ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE) ≤ # buf2 + # buf9, (ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE) * m ≤ n0, 2 * ENCODED_NAT_SIZE + # buf2 + ENCODED_VOLID_SIZE ≤ # buf4, ENCODED_NAT_SIZE + # buf2 + ENCODED_VOLID_SIZE ≤ # buf4, ENCODED_VOLID_SIZE ≤ # buf9, m * (ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE) + ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE ≤ # buf9, vtbl1 ⊥ vtbl, err0 = ESUCCESS → is-encoded(#(vtbl1 ∪ vtbl), subarray(buf4, 0, ENCODED_NAT_SIZE)) ∧ n1 = ENCODED_NAT_SIZE, err0 = ESUCCESS ∨ ⌊err0⌋ ⊦ vtbl1 = ∅, v ∈ vtbl, (v0 ∈ vtbl1 ∨ v0 ∈ vtbl → v0 ≠ v ∧ v0 ∈ vtbl1 ∨ v0 ∈ vtbl[v, vtbl1[v]]) ∧ (vtbl1 ∪ vtbl)[v0] = ((vtbl1 -- v) ∪ vtbl[v, vtbl1[v]])[v0]

User applied rule case distinction

And obtained the following new goals

Proof step 129:
# buf10 = 0, # buf3 = 0, # buf2 = # vtbl * (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE), # buf0 = ENCODED_NAT_SIZE, # buf8 = ENCODED_VOLID_SIZE, # buf = 0, # buf1 = 0, # vtbl1 = m + 1, # buf7 = ENCODED_NAT_SIZE, # buf11 = 0, # buf4 = 2 * ENCODED_NAT_SIZE + n0 + # buf2 + ENCODED_VOLID_SIZE, ENCODED_NAT_SIZE + # buf2 + # buf9 = # buf4, ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE + n0 = # buf9, ENCODED_NAT_SIZE = # buf5, is-encoded(vtbl1[v], subarray(buf9, ENCODED_VOLID_SIZE, ENCODED_NAT_SIZE)), is-encoded(v, subarray(buf9, 0, ENCODED_VOLID_SIZE)), is-encoded(#(vtbl1 ∪ vtbl), buf0), is-encoded-rec(vtbl, buf2), v ∈ vtbl1, m * (ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE) + ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE ≤ # buf9, ENCODED_VOLID_SIZE ≤ # buf9, ENCODED_NAT_SIZE + # buf2 + ENCODED_VOLID_SIZE ≤ # buf4, 2 * ENCODED_NAT_SIZE + # buf2 + ENCODED_VOLID_SIZE ≤ # buf4, (ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE) * m ≤ n0, #(vtbl1 ∪ vtbl) * (ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE) ≤ # buf2 + # buf9, ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE ≤ # buf9, vtbl1 ⊥ vtbl, err0 = ESUCCESS → is-encoded(#(vtbl1 ∪ vtbl), subarray(buf4, 0, ENCODED_NAT_SIZE)) ∧ n1 = ENCODED_NAT_SIZE, err0 = ESUCCESS ∨ ⌊err0⌋ ⊦ (vtbl1 ∪ vtbl)[v0] = ((vtbl1 -- v) ∪ vtbl[v, vtbl1[v]])[v0], vtbl1 = ∅, v ∈ vtbl

Rule argument

pos: right 3

Additional information

Used simplifier rules: ⊦ v ∈ vtbl[v0, n] ↔ v = v0 ∨ v ∈ vtbl; (ws)