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Proof step 1 from proof inapp-11 (conclusion)

⊦ x + y = z + a ' ∧ b ∈ x ∧ a ≠ b → b ∈ z

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
x + y = z + a ', b ∈ x, a ∈ x ∨ a ∈ y ⊦ a = b, 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);