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Proof step 5 from proof sorted-shift-one (previous step)

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

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 6:
n1 = m + 1, A[n1 + 1] < A[m + 1, A[m]][n1], n1 + 1 < n0, n1 + 1 < # A, m + 1 < n0, m + 1 < # A, n ≤ m, n0 ≤ # A, n ≤ n1, ∀ n1. n ≤ n1 ∧ n1 + 1 < n0 → ¬ A[n1 + 1] < A[n1] ⊦ n1 = m
Proof step 10:
A[n1 + 1] < A[m + 1, A[m]][n1], n1 + 1 < n0, n1 + 1 < # A, m + 1 < n0, m + 1 < # A, n ≤ m, n0 ≤ # A, n ≤ n1, ∀ n1. n ≤ n1 ∧ n1 + 1 < n0 → ¬ A[n1 + 1] < A[n1] ⊦ n1 = m, n1 = m + 1

Rule argument

fma: n1 = m + 1

Additional information

Used formulas: n1 = m + 1