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Proof step 8 from proof firstn-prefix (previous step)

n = m + 1, n ≤ # x0 + 1, ∀ n. n ≤ # x0 → firstn(n, x0) ⊑ x0 ⊦ n = 0, firstn(m, x0) ⊑ x0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
m ≤ # x0, ∀ n. n ≤ # x0 → firstn(n, x0) ⊑ x0 ⊦ firstn(m, x0) ⊑ x0

Rule argument

Additional information

Used simplifier rules: lep-02: ⊦ m + n ≤ m + n0 ↔ n ≤ n0; from specification nat%c: ⊦ m + n = n + m; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%oz: ⊦ m + 1 ≠ 0; from specification nat-basic2