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Proof step 4 from proof subarray-split-first (previous step)

n1 = m + 1, n0 + n1 ≤ # ar ⊦ n1 = 0, subarray(ar, n0, n1) = mkarray(1)[0, ar[n0]] + subarray(ar, n0 + 1, m)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
n0 + m < # ar ⊦ subarray(ar, n0, m + 1) = mkarray(1)[0, ar[n0]] + subarray(ar, n0 + 1, m)

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m + 1 ≤ n ↔ m < n; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + 1 ≠ 0; (s)