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Proof step 13 from proof perm-put (previous step)

¬(perm(x -1l a, y[n, a] -1l a) ∧ a ∈ x ∧ a ∈ y[n, a]), perm(x -1l a, y -1l y[n]), a ∈ x, n < # y, perm(y -1l y[n], x -1l a) ⊦ y = [], perm(x, y[n, a])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 14:
perm(y -1l y[n], x -1l a), n < # y, a ∈ x, perm(x -1l a, y -1l y[n]) ⊦ y = [], perm(x -1l a, y[n, a] -1l a), perm(x, y[n, a])

Rule argument

Additional information

Used simplifier rules: sym-02: ⊦ ¬ perm(x, y) → ¬ perm(y, x);%sym-02: ⊦ ¬ perm(x, y) → ¬ perm(y, x);%put-in-02: ⊦ m < # x → a ∈ x[m, a]; from specification list-del