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Proof step 3 from proof sorted-insert-merge (previous step)

A[m, a][n0 + 1] < A[m, a][n0], n0 + 1 < n, n0 + 1 < # A, n ≤ # A, m ≤ # A, ∀ n0. m < n0 ∧ n0 + 1 < n → ¬ A[n0 + 1] < A[n0], ∀ n0. n0 + 1 < m → ¬ A[n0 + 1] < A[n0] ⊦ m = 0, A[m + 1] < a, a < A[m - 1], A[m + 1] < A[m - 1]

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 4:
m = m0 + 1, n0 + 1 < # A, n0 + 1 < n, A[m, a][n0 + 1] < A[m, a][n0], m ≤ # A, n ≤ # A, ∀ n0. n0 + 1 < m → ¬ A[n0 + 1] < A[n0], ∀ n0. m < n0 ∧ n0 + 1 < n → ¬ A[n0 + 1] < A[n0] ⊦ m = 0, A[m + 1] < A[m0], a < A[m0], A[m + 1] < a

Rule argument

spec: nat name: elim-pred-c seq: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1 subst: [n, m] → [m, m0]

Additional information

Used simplifier rules: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1; (elim) Used terms: m, m0