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Proof step 8 from proof Inv-last-inner-init-b (previous step)

# A = # A0, i + 1 < # A0, m < i, m < # A0, perm(A[m + 1, y][2 + m, x], A0), sorted(A, 3 + m, i + 2), sorted(A, 0, m + 1), i ≤ # A0, m + 1 ≠ i → ¬ A[3 + m] < A[m], m + 1 ≠ i → x < A[3 + m] ⊦ x < y, x < A[m], perm(A[2 + m, x][m + 1, y], A0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
m ≠ n ⊦ ar[m, a][n, b] = ar[n, b][m, a]

Rule argument

spec: array name: cputput-reverse seq: m ≠ n ⊦ ar[m, a][n, b] = ar[n, b][m, a] subst: [b, n, a, m, ar] → [y, m + 1, x, 2 + m, A] flags: <all paths>

Additional information

Used simplifier rules: ⊦ m + n = m + n0 ↔ n = n0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic Used terms: y, m + 1, x, 2 + m, A