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Proof step 12 from proof prefixn-split-dropn (previous step)

# y = n0 + n1 ⊦ y = firstn(n0, y) + firstn(n1, restn(n0, y) + z)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: list-del name: first-append-01 seq: ⊦ n + m ≤ # x → firstn(m, restn(n, x) + y) = firstn(m, restn(n, x)) subst: [y, x, n, m] → [z, y, n0, n1] flags: <all paths>

Additional information

Used simplifier rules: a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ # x = n0 + m0 → firstn(m0, x) + firstn(n0, restn(m0, x)) = x; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ 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%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic% ⊦ m < n → n ≠ 0; (s)% ⊦ m < n → ¬ n < m; (s) Used terms: z, y, n0, n1