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Proof step 7 from proof filt-dups (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
dups(filter(x0, y)), ∀ y0. ¬ dups(filter(x0, y0)) ⊦ a ∈ y, a ∈ x0, dups(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