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Proof step 10 from proof f-rm (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 11:
a ∈ y, ∀ y. filter(rmdup(x0), y) = rmdup(filter(x0, y)) ⊦ filter(rmdup(x0), y) = rmdup(filter(x0, y)), a ∈ x0

Rule argument

Additional information

Used simplifier rules: filt-y: ⊦ a ∈ y → filter(a ' + x, y) = a ' + filter(x, y);%app-01: ⊦ x + y = x + z ↔ y = z; from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list%c: ⊦ a + x = a ' + x; from specification list%rmdup-n: ⊦ ¬ a ∈ x → rmdup(a ' + x) = a + rmdup(x); from specification list-dup