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Proof step 7 from proof f-rm (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
a ∈ y, ∀ y. filter(rmdup(x0), y) = rmdup(filter(x0, y)) ⊦ filter(rmdup(a ' + x0), y) = a ' + rmdup(filter(x0, y)), a ∈ filter(x0, y)

Rule argument

Additional information

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