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Proof step 29 from proof encode-contract (previous step)

# subarray(buf1, n, ENCODED_ELEM_SIZE) = # mkempbuf(ENCODED_ELEM_SIZE), # 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, ∀ n0. n0 < # subarray(buf1, n, ENCODED_ELEM_SIZE) → subarray(buf1, n, ENCODED_ELEM_SIZE)[n0] = mkempbuf(ENCODED_ELEM_SIZE)[n0] ⊦ n0 + ENCODED_ELEM_SIZE = 0, buf1[n1] = empty

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 30:
# buf1 = # buf, # buf = n0 + n + ENCODED_ELEM_SIZE, 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, ∀ n2. n2 < ENCODED_ELEM_SIZE → buf1[n + n2] = empty ⊦ n0 + ENCODED_ELEM_SIZE = 0, buf1[n1] = empty

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → mkempbuf(n)[m] = empty; (s)% ⊦ n0 < n → subarray(buf, m, n)[n0] = buf[m + n0]; (s)% ⊦ # mkempbuf(n) = n; (s)% ⊦ # subarray(buf, m, n) = n; (s)