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Proof step 2 from proof dups-lesize (previous step)

# y < # x, ∀ a. a ∈ x → a ∈ y ⊦ x = [], dups(x), dups(y)

User applied rule structural induction

And obtained the following new goals

Proof step 3:
∀ y. # y < # x0 ∧ (∀ a. a ∈ x0 → a ∈ y) → x0 = [] ∨ dups(x0) ∨ dups(y), # y < #(a + x0), ∀ a0. a0 ∈ a + x0 → a0 ∈ y ⊦ a + x0 = [], dups(a + x0), dups(y)

Rule argument

indvar: x

Additional information

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