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Proof step 2 from proof inapp-12 (previous step)

x + y = z + a ', b ∈ x ⊦ y = [], b ∈ z

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
x + y = z + a ', b ∈ x, a ∈ y ⊦ y = [], b ∈ z

Rule argument

Additional information

Used simplifier rules: in-15: ⊦ x + a ' = y → a ∈ y;%a: ⊦ (x + y) + z = x + y + z;%in-append: ⊦ a ∈ x + y ↔ a ∈ x ∨ a ∈ y;%ni: ⊦ x + a ' = y + z ∧ ¬ a ∈ z → z = [];