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Proof step 1 from proof sorted-write-other (conclusion)

m ≤ n0 ⊦ sorted(ar[n0, a], n, m) ↔ sorted(ar, n, m)

Heuristic simplifier applied rule simplifier

And closed the goal!

Rule argument

Additional information

Used simplifier rules: sorted: ⊦ sorted(ar, n, m) ↔ m ≤ # ar ∧ (∀ n0. n ≤ n0 ∧ n0 + 1 < m → ar[n0] ≤ ar[n0 + 1]);%less-eq-elem: ⊦ x ≤ y ↔ ¬ y < x;% ⊦ m ≤ n → (n < m ↔ false); (s)%m ≠ n ⊦ ar[m, a][n] = ar[n]; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ ¬ m + n < m; (s)% ⊦ m < n → n ≠ 0; (s)%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ # ar[n, a] = # ar; (s)