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Proof step 7 from proof in-02 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
a ∈ x0 -l a, ∀ a. ¬ a ∈ x0 -l a ⊦ a = a0

Rule argument

Additional information

Used simplifier rules: del-n: ⊦ a ≠ b → (b ' + x) -l a = b ' + (x -l a);%in-01: ⊦ a ≠ b → (a ∈ b ' + x ↔ a ∈ x); from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list