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Proof step 31 from proof encode-contract (previous step)

# buf = n0 + n + ENCODED_ELEM_SIZE, # buf1 = # buf, subarray(buf1, 0, n) = subarray(buf, 0, n), subarray(buf1, n + ENCODED_ELEM_SIZE, n0) = subarray(buf, n + ENCODED_ELEM_SIZE, n0), n < # buf, n1 < # buf, n1 < n + ENCODED_ELEM_SIZE, is-encoded(a, subarray(buf1, n, ENCODED_ELEM_SIZE)), n ≤ n1, n + ENCODED_ELEM_SIZE ≤ # buf, n1 - n < ENCODED_ELEM_SIZE → buf1[n + (n1 - n)] = empty ⊦ n0 + ENCODED_ELEM_SIZE = 0, buf1[n1] = empty

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 32:
# buf1 = # buf, # buf = n0 + n + ENCODED_ELEM_SIZE, buf1[n + (n1 - n)] = empty, subarray(buf1, n + ENCODED_ELEM_SIZE, n0) = subarray(buf, n + ENCODED_ELEM_SIZE, n0), subarray(buf1, 0, n) = subarray(buf, 0, n), n1 < n + ENCODED_ELEM_SIZE, n1 < # buf, n < # buf, is-encoded(a, subarray(buf1, n, ENCODED_ELEM_SIZE)), n + ENCODED_ELEM_SIZE ≤ # buf, n ≤ n1 ⊦ n0 + ENCODED_ELEM_SIZE = 0, buf1[n1] = empty

Rule argument

Additional information

Used simplifier rules: c: ⊦ m + n = n + m; from specification nat-basic%n0 ≤ n ⊦ n - n0 < m ↔ n < m + n0; (s)% ⊦ m ≤ n → (n < m ↔ false); (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)