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Proof step 3 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) ∧ perm(A[1, x][0, y], A0)

User applied rule case distinction

And obtained the following new goals

Proof step 4:
# 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)
Proof step 9:
# 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, perm(A[1, x][0, y], A0)

Rule argument

pos: right 2

Proof step 3 from proof Inv-last-inner-init-a (previous step)

User applied rule case distinction

And obtained the following new goals

Rule argument

Additional information