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Proof step 5 from proof inapp (previous step)

a ' + x + b ' = y + c ' + c ' + z, a ∈ y, z ≠ [] → (∃ y, a. z = y + a '), b ∈ y ∨ b = c ∨ b ∈ z ⊦ a = b, dups(x), b ∈ x, a ∈ x

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information