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Proof step 14 from proof f-rm (previous step)

a ∈ x0 ∧ a ∈ y, a ∈ y, ∀ y. filter(rmdup(x0), y) = rmdup(filter(x0, y)) ⊦ filter(rmdup(a ' + x0), y) = rmdup(filter(x0, y))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
a ∈ x0, a ∈ y, ∀ y. filter(rmdup(x0), y) = rmdup(filter(x0, y)) ⊦ filter(rmdup(x0), y) = rmdup(filter(x0, y))

Rule argument

Additional information

Used simplifier rules: a: ⊦ (x + y) + z = x + y + z; from specification list%rmdup-y: ⊦ a ∈ x → rmdup(a ' + x) = rmdup(x); from specification list-dup