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Proof step 2 from proof perm-switch (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
m < # y, n < # y ⊦ perm(x, y[m, y[n]][n, y[m]]) ↔ perm(x, y), y = []

Rule argument

Additional information

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