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Proof step 5 from proof sorted-inc-right (previous step)

n0 < # ar, n < # ar, n + 1 < # ar, n0 + 1 < # ar, m0 + 1 < # ar, ar[m0 + 1, a][n0 + 1] < ar[n0], n ≤ n0, n0 ≤ m0, n ≤ m0, ∀ n1. n ≤ n1 ∧ n1 < m0 → ¬ ar[n1 + 1] < ar[n1] ⊦ a < ar[m0]

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 6:
ar[m0 + 1, a][n0 + 1] < ar[n0], m0 + 1 < # ar, n0 + 1 < # ar, n + 1 < # ar, n < # ar, n0 < # ar, n ≤ m0, n0 ≤ m0, n ≤ n0, ∀ n1. n ≤ n1 ∧ n1 < m0 → ¬ ar[n1 + 1] < ar[n1] ⊦ n0 + 1 = m0 + 1, a < ar[m0]

Rule argument

fma: n0 + 1 = m0 + 1

Additional information

Used simplifier rules: ⊦ m + n = m + n0 ↔ n = n0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic% ⊦ m < # ar → ar[m, a][m] = a; (s)% ⊦ m ≤ m; (s) Used formulas: n0 + 1 = m0 + 1