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Proof step 3 from proof filt-dups (previous step)

∀ y. dups(filter(x0, y)) → dups(x0), dups(filter(a + x0, y)) ⊦ dups(a + x0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
dups(filter(a ' + x0, y)), ∀ y0. ¬ dups(filter(x0, y0)) ⊦ a ∈ x0, dups(x0)

Rule argument

Additional information

Used simplifier rules: a: ⊦ (x + y) + z = x + y + z; from specification list%rec: ⊦ dups(a ' + x) ↔ ¬ ¬(a ∈ x ∨ dups(x)); from specification list-dup%c: ⊦ a + x = a ' + x; from specification list