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Proof step 7 from proof Inv-last-inner-init-a (previous step)

# A = # A0, A[2] < x, perm(A[0, y][1, x], A0) ⊦ # A0 = 1, # A0 = 0, x < y, sorted(A[1, x], 1, 2)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: oarray-sorted name: sorted-0-or-1 seq: 1 ≤ # ar, n0 ≤ # ar, n0 - n ≤ 1 ⊦ sorted(ar, n, n0) subst: [n0, n, ar] → [2, 1, A[1, x]] flags: <all paths>

Additional information

Used simplifier rules: ⊦ # ar[n, a] = # ar; (s)% ⊦ m ≠ n → (m ≤ n ↔ m < n); (s)% ⊦ 1 < m ↔ ¬(m = 0 ∨ m = 1); (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ m < 1 ↔ m = 0; (s)% ⊦ m ≠ 0 → (m < 2 ↔ m = 1); (s)%1 ≤ # ar, n0 ≤ # ar, n0 - n ≤ 1 ⊦ sorted(ar, n, n0); (ss) Used terms: 2, 1, A[1, x]