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Proof step 1 from proof list2set-append (conclusion)

⊦ list2set(x + y) = list2set(x) ∪ list2set(y)

User applied rule structural induction

And obtained the following new goals

Proof step 2:
∀ y. list2set(x0 + y) = list2set(x0) ∪ list2set(y) ⊦ list2set((a + x0) + y) = list2set(a + x0) ∪ list2set(y)

Rule argument

indvar: x

Additional information

Used simplifier rules: list2set-empty: ⊦ list2set([]) = ∅;%list freely generated by [], +;;% ⊦ [] + x = x;% ⊦ (x + y) + z = x + y + z;% ⊦ s ∪ ∅ = s;% ⊦ (s ∪ s0) ∪ s1 = s ∪ s0 ∪ s1;% ⊦ s ∪ s0 = s0 ∪ s;