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Proof step 16 from proof encode-contract (previous step)

# buf1 = n0 + ENCODED_ELEM_SIZE, # buf = n0 + ENCODED_ELEM_SIZE, subarray(buf1, ENCODED_ELEM_SIZE, n0) = subarray(buf, ENCODED_ELEM_SIZE, n0), is-encoded-nonempty(a, subarray(buf1, 0, ENCODED_ELEM_SIZE)), EB_PAGE_SIZE ≤ n0 + ENCODED_ELEM_SIZE, ENCODED_ELEM_SIZE ≤ EB_PAGE_SIZE ⊦ is-encoded-nonempty(a, subarray(subarray(buf1, 0, EB_PAGE_SIZE), 0, ENCODED_ELEM_SIZE)) ∧ subarray(buf1, 0, EB_PAGE_SIZE) ≠ emptypage

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 17:
⊦ n0 + n1 ≤ # buf ∧ m0 + m1 ≤ n1 → subarray(subarray(buf, n0, n1), m0, m1) = subarray(buf, n0 + m0, m1)
Proof step 18:
# buf = n0 + ENCODED_ELEM_SIZE, # buf1 = n0 + ENCODED_ELEM_SIZE, subarray(buf1, ENCODED_ELEM_SIZE, n0) = subarray(buf, ENCODED_ELEM_SIZE, n0), is-encoded-nonempty(a, subarray(buf1, 0, ENCODED_ELEM_SIZE)), ENCODED_ELEM_SIZE ≤ EB_PAGE_SIZE, EB_PAGE_SIZE ≤ n0 + ENCODED_ELEM_SIZE, 0 + EB_PAGE_SIZE ≤ # buf1, 0 + ENCODED_ELEM_SIZE ≤ EB_PAGE_SIZE ⊦ is-encoded-nonempty(a, subarray(buf1, 0 + 0, ENCODED_ELEM_SIZE)) ∧ subarray(buf1, 0, EB_PAGE_SIZE) ≠ emptypage

Rule argument

spec: array-copy, inst: buffer name: subarray-subarray-elim seq: ⊦ n0 + n1 ≤ # buf ∧ m0 + m1 ≤ n1 → subarray(subarray(buf, n0, n1), m0, m1) = subarray(buf, n0 + m0, m1) subst: [m1, m0, n1, n0, buf] → [ENCODED_ELEM_SIZE, 0, EB_PAGE_SIZE, 0, buf1] flags: <all paths>

Additional information

Used simplifier rules: ⊦ n + 0 = n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m = m + n ↔ n = 0; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat% ⊦ EB_PAGE_SIZE ≠ 0; (s)% ⊦ m ≤ n → (n < m ↔ false); (s)%# buf = n ⊦ subarray(buf, 0, n) = buf; (s)% ⊦ m ≠ n → (m ≤ n ↔ m < n); (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat%is-encoded-size: ⊦ is-encoded-nonempty(a, buf) → # buf = ENCODED_ELEM_SIZE; (forward) from specification encoding-fixed-size-nonempty%lf: ⊦ m < n ∧ n < n0 → m +1 < n0; (forward) from specification nat-basic%trans: ⊦ n < n0 ∧ n0 < n1 → n < n1; (forward) from specification nat-basic% ⊦ m < n → n ≠ 0; (s)% ⊦ m < n → ¬ n < m; (s)% ⊦ is-encoded-nonempty(a, buf) → (is-encoded-nonempty(b, buf) ↔ a = b); (s)% ⊦ # emptypage = EB_PAGE_SIZE; (s) Used terms: ENCODED_ELEM_SIZE, 0, EB_PAGE_SIZE, 0, buf1