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Proof step 3 from proof sorted-shift-one (previous step)

n1 + 1 < # A, n1 + 1 < n0, A[m + 1, A[m]][n1 + 1] < A[m + 1, A[m]][n1], m + 1 < # A, m + 1 < n0, n ≤ n1, n0 ≤ # A, n ≤ m, ∀ n1. n ≤ n1 ∧ n1 + 1 < n0 → ¬ A[n1 + 1] < A[n1] ⊦

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 4:
m + 1 < n0, m + 1 < # A, A[m + 1, A[m]][n1 + 1] < A[m + 1, A[m]][n1], n1 + 1 < n0, n1 + 1 < # A, n ≤ m, n0 ≤ # A, n ≤ n1, ∀ n1. n ≤ n1 ∧ n1 + 1 < n0 → ¬ A[n1 + 1] < A[n1] ⊦ n1 + 1 = m + 1

Rule argument

fma: n1 + 1 = m + 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% ⊦ m = m + n ↔ n = 0; (s)%m ≠ n ⊦ ar[m, a][n] = ar[n]; (s)% ⊦ m < # ar → ar[m, a][m] = a; (s)% ⊦ ¬ a < a; (s) Used formulas: n1 + 1 = m + 1