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Proof step 1 from proof perm-switch (conclusion)

⊦ m < # y ∧ n < # y ∧ a = y[n] ∧ b = y[m] → (perm(x, y[m, a][n, b]) ↔ perm(x, y))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
n < # y, m < # y ⊦ perm(x, y[m, y[n]][n, y[m]]) ↔ perm(x, y), y = []

Rule argument

Additional information

Used simplifier rules: l: ⊦ # x = 0 ↔ x = []; from specification list-data%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic1