| # buf6 = # buf4, # 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(buf6, 0, (ENCODED_NAT_SIZE + # buf2) + ENCODED_VOLID_SIZE) = subarray(buf5, 0, (ENCODED_NAT_SIZE + # buf2) + ENCODED_VOLID_SIZE), subarray(buf6, 2 * ENCODED_NAT_SIZE + # buf2 + ENCODED_VOLID_SIZE, # buf4 - 2 * ENCODED_NAT_SIZE + # buf2 + ENCODED_VOLID_SIZE) = subarray(buf5, 2 * ENCODED_NAT_SIZE + # buf2 + ENCODED_VOLID_SIZE, # buf4 - 2 * ENCODED_NAT_SIZE + # buf2 + ENCODED_VOLID_SIZE), 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), is-encoded(v, subarray(buf5, ENCODED_NAT_SIZE + # buf2, ENCODED_VOLID_SIZE)), is-encoded(#(vtbl1 ∪ vtbl), buf0), is-encoded-rec(vtbl, buf2), v ∈ 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, 2 * ENCODED_NAT_SIZE + # buf2 + ENCODED_VOLID_SIZE ≤ # buf4, vtbl1 ⊥ vtbl, err = ESUCCESS → is-encoded(vtbl1[v], subarray(buf6, (ENCODED_NAT_SIZE + # buf2) + ENCODED_VOLID_SIZE, ENCODED_NAT_SIZE)) ∧ n3 = ENCODED_NAT_SIZE, err0 = ESUCCESS → is-encoded(#(vtbl1 ∪ vtbl), subarray(buf4, 0, ENCODED_NAT_SIZE)) ∧ n1 = ENCODED_NAT_SIZE, err = ESUCCESS ∨ ⌊err⌋ , err0 = ESUCCESS ∨ ⌊err0⌋ ⊦ ⟪vtbl0 := vtbl1 -- v⟫ ( (err = ESUCCESS ∨ ⌊err⌋ ) ∧ ( err = ESUCCESS → (∃ buf0, buf1, buf, vtbl3. buf6 = buf0 + buf1 + buf ∧ vtbl1 ∪ vtbl = vtbl0 ∪ vtbl3 ∧ vtbl0 ⊥ vtbl3 ∧ # buf0 + # buf1 = ((ENCODED_NAT_SIZE + # buf2) + ENCODED_VOLID_SIZE) + n3 ∧ # vtbl0 * (ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE) ≤ # buf ∧ is-encoded(#(vtbl0 ∪ vtbl3), buf0) ∧ is-encoded-rec(vtbl3, buf1))) ∧ # vtbl0 < # vtbl1), vtbl1 = ∅, v ∈ vtbl |
# 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, # buf6 = # 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, subarray(buf6, 2 * ENCODED_NAT_SIZE + # buf2 + ENCODED_VOLID_SIZE, # buf4 - 2 * ENCODED_NAT_SIZE + # buf2 + ENCODED_VOLID_SIZE) = subarray(buf5, 2 * ENCODED_NAT_SIZE + # buf2 + ENCODED_VOLID_SIZE, # buf4 - 2 * ENCODED_NAT_SIZE + # buf2 + ENCODED_VOLID_SIZE), subarray(buf6, 0, (ENCODED_NAT_SIZE + # buf2) + ENCODED_VOLID_SIZE) = subarray(buf5, 0, (ENCODED_NAT_SIZE + # buf2) + ENCODED_VOLID_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, 2 * ENCODED_NAT_SIZE + # buf2 + ENCODED_VOLID_SIZE ≤ # buf4, #(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, err = ESUCCESS → is-encoded(vtbl1[v], subarray(buf6, (ENCODED_NAT_SIZE + # buf2) + ENCODED_VOLID_SIZE, ENCODED_NAT_SIZE)) ∧ n3 = ENCODED_NAT_SIZE, err0 = ESUCCESS ∨ ⌊err0⌋ , err = ESUCCESS ∨ ⌊err⌋ ⊦ vtbl1 = ∅, v ∈ vtbl, (err = ESUCCESS ∨ ⌊err⌋ ) ∧ ( err = ESUCCESS → (∃ buf0, buf1, buf, vtbl3. buf6 = buf0 + buf1 + buf ∧ vtbl1 ∪ vtbl = (vtbl1 -- v) ∪ vtbl3 ∧ vtbl1 -- v ⊥ vtbl3 ∧ # buf0 + # buf1 = ((ENCODED_NAT_SIZE + # buf2) + ENCODED_VOLID_SIZE) + n3 ∧ #(vtbl1 -- v) * (ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE) ≤ # buf ∧ is-encoded(#((vtbl1 -- v) ∪ vtbl3), buf0) ∧ is-encoded-rec(vtbl3, buf1))) ∧ #(vtbl1 -- v) < # vtbl1