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Proof step 2 from proof del1 (previous step)

⊦ filter(x, y -1l a) = filter(x, y), a ∈ x

Heuristic structural induction applied rule structural induction

And obtained the following new goals

Proof step 3:
∀ y, a. filter(x0, y -1l a) = filter(x0, y) ∨ a ∈ x0 ⊦ filter(a0 + x0, y -1l a) = filter(a0 + x0, y), a ∈ a0 + x0

Rule argument

term: x

Additional information

Used simplifier rules: filt-e: ⊦ filter([], y) = [];%list freely generated by [], +;;