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Proof step 6 from proof filt-dups (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
dups(filter(x0, y)), a ∈ y, ∀ y0. ¬ dups(filter(x0, y0)) ⊦ dups(x0), a ∈ x0

Rule argument

Additional information

Used simplifier rules: filt-y: ⊦ a ∈ y → filter(a ' + x, y) = a ' + filter(x, y);%filt-in: ⊦ a ∈ filter(x, y) ↔ a ∈ x ∧ a ∈ y;% ⊦ dups(a ' + x) ↔ a ∈ x ∨ dups(x); (s)%a: ⊦ (x + y) + z = x + y + z; from specification list