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Proof step 27 from proof encode-contract (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 28:
# buf = n0 + ENCODED_ELEM_SIZE, # buf1 = n0 + ENCODED_ELEM_SIZE, subarray(buf1, ENCODED_ELEM_SIZE, n0) = subarray(buf, ENCODED_ELEM_SIZE, n0), n < EB_PAGE_SIZE, n < ENCODED_ELEM_SIZE, n < n0 + ENCODED_ELEM_SIZE, is-encoded(a, subarray(buf1, 0, ENCODED_ELEM_SIZE)), EB_PAGE_SIZE ≤ n0 + ENCODED_ELEM_SIZE, ENCODED_ELEM_SIZE ≤ EB_PAGE_SIZE, ∀ n. n < EB_PAGE_SIZE → buf1[n] = empty ⊦ buf1[n] = empty

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic% ⊦ EB_PAGE_SIZE ≠ 0; (s)% ⊦ ENCODED_ELEM_SIZE ≠ 0; (s)%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m < n → mkempbuf(n)[m] = empty; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ n + 0 = n; (s)% ⊦ n0 < n → subarray(buf, m, n)[n0] = buf[m + n0]; (s)% ⊦ # mkempbuf(n) = n; (s)% ⊦ # subarray(buf, m, n) = n; (s)