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Proof step 4 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)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
a ≤ ar[n + 1] ⊦ sorted(ar, n + 1, m) → sorted(ar[n, a], n, m)
Proof step 6:
# 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)

Rule argument

spec: oarray-sorted name: sorted-inc-left seq: a ≤ ar[n + 1] ⊦ sorted(ar, n + 1, m) → sorted(ar[n, a], n, m) subst: [m, a, n, ar] → [i + 2, x, 1, A] flags: <all paths>

Additional information

Used terms: i + 2, x, 1, A