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Proof step 3 from proof in-02 (previous step)

∀ a. ¬ a ∈ x0 -l a, a ∈ (a0 + x0) -l a ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
a ∈ (a0 ' + x0) -l a, ∀ a. ¬ a ∈ x0 -l a ⊦

Rule argument

Additional information

Used simplifier rules: c: ⊦ a + x = a ' + x; from specification list