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Proof step 6 from proof Inv-last-inner-init-a (previous step)

# A = # A0, i + 1 < # A0, perm(A[0, y][1, x], A0), sorted(A, 2, i + 2), i ≤ # A0, 0 ≠ i → x < A[2] ⊦ x < y, sorted(A[1, x], 1, i + 2), x ≤ A[1 + 1] ∧ sorted(A, 1 + 1, i + 2)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: ⊦ 1 < m ↔ ¬(m = 0 ∨ m = 1); (s)% ⊦ 0 ≤ m; (s)%1 ≤ # ar, n0 ≤ # ar, n0 - n ≤ 1 ⊦ sorted(ar, n, n0); (as)% ⊦ m < n → (m + n < 2 ↔ m = 0 ∧ n = 1); (ws)% ⊦ m +1 = m + 1; (s)%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat%trans: ⊦ n < n0 ∧ n0 < n1 → n < n1; (forward) from specification nat-basic%lf: ⊦ m < n ∧ n < n0 → m +1 < n0; (forward) from specification nat-basic%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ a < b → (b < a ↔ false); (ss)% ⊦ m < n → n ≠ 0; (s)% ⊦ m < 1 ↔ m = 0; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ ¬ a < a; (s)%nll: ⊦ ¬ b < a ∧ b < c → a < c; (forward) from specification oelem%transitivity: ⊦ a < b ∧ b < c → a < c; (forward) from specification oelem%m ≤ m0 ⊦ sorted(A, m, n) → sorted(A, m0, n); (ss)% ⊦ x ≤ y ↔ ¬ y < x; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic