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Proof step 12 from proof perm-put (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ perm(x -1l a, y -1l a) ∧ a ∈ x ∧ a ∈ y → perm(x, y)
Proof step 14:
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]

Rule argument

spec: <toplevel> name: del-02 seq: ⊦ perm(x -1l a, y -1l a) ∧ a ∈ x ∧ a ∈ y → perm(x, y) subst: [a, y, x] → [a, y[n, a], x] flags: <all paths>

Additional information

Used terms: a, y[n, a], x