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Proof step 1 from proof perm-last-rec (conclusion)

⊦ perm(x, y + a ') ↔ a ∈ x ∧ perm(x -1l a, y)

User applied rule structural induction

And obtained the following new goals

Proof step 2:
⊦ perm(x, [] + a ') ↔ a ∈ x ∧ perm(x -1l a, [])
Proof step 5:
∀ x, a. perm(x, y0 + a ') ↔ a ∈ x ∧ perm(x -1l a, y0) ⊦ perm(x, (a0 + y0) + a ') ↔ a ∈ x ∧ perm(x -1l a, a0 + y0)

Rule argument

indvar: y

Additional information

Used simplifier rules: list freely generated by [], +;;