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Proof step 8 from proof filt-dups (previous step)

dups(filter(a ' + x0, y)), ∀ y0. ¬ dups(filter(x0, y0)) ⊦ dups(x0), a ∈ x0, a ∈ y

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
dups(filter(x0, y)), ∀ y0. ¬ dups(filter(x0, y0)) ⊦ dups(x0), a ∈ y, a ∈ x0

Rule argument

Additional information

Used simplifier rules: filt-n: ⊦ ¬ a ∈ y → filter(a ' + x, y) = filter(x, y);%a: ⊦ (x + y) + z = x + y + z; from specification list