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Proof step 14 from proof perm-put (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
n < # y, perm(y -1l y[n], x -1l a), perm(x -1l a, y -1l y[n]), a ∈ x ⊦ 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);% ⊦ m < # x → a ∈ x[m, a]; (s)