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Proof step 5 from proof filt-dups (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
a ∈ y, dups(filter(x0, y)), ∀ y0. ¬ dups(filter(x0, y0)) ⊦ a ∈ x0, dups(x0)

Rule argument

Additional information

Used simplifier rules: filt-y: ⊦ a ∈ y → filter(a ' + x, y) = a ' + filter(x, y);%in-01-01: ⊦ a ∈ y → (a ∈ filter(x, y) ↔ a ∈ x);%rec: ⊦ dups(a ' + x) ↔ ¬ ¬(a ∈ x ∨ dups(x)); from specification list-dup%a: ⊦ (x + y) + z = x + y + z; from specification list