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Proof step 2 from proof checksum-append-left (previous step)

n ≤ # buf0 ⊦ checksum(buf0 + buf1, n) = checksum(buf0, n)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: checksum-prefix seq: ⊦ n ≤ # buf0 ∧ n ≤ # buf1 ∧ subarray(buf0, 0, n) = subarray(buf1, 0, n) → checksum(buf0, n) = checksum(buf1, n) subst: [buf1, n, buf0] → [buf0, n, buf0 + buf1] flags: <all paths>

Additional information

Used simplifier rules: ⊦ #(buf + buf0) = # buf + # buf0; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ 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 ≤ n ↔ ¬ n < m; (ss)% ⊦ m ≤ n → (n < m ↔ false); (s)%n + m ≤ # buf ⊦ subarray(buf + buf0, n, m) = subarray(buf, n, m); (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat% ⊦ m < n → n ≠ 0; (s)% ⊦ ¬ m + n < m; (s) Used terms: buf0, n, buf0 + buf1