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Proof step 6 from proof perm-put (previous step)

n < # y, perm(y[n, a], x), perm(x, y[n, a]) ⊦ y = [], a ∈ x

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ a ∈ y ∧ ¬ a ∈ x → ¬ perm(x, y)

Rule argument

spec: <toplevel> name: in seq: ⊦ a ∈ y ∧ ¬ a ∈ x → ¬ perm(x, y) subst: [a, y, x] → [a, y[n, a], x] flags: <all paths>

Additional information

Used simplifier rules: ⊦ m < # x → a ∈ x[m, a]; (s) Used terms: a, y[n, a], x