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Proof step 2 from proof isin-01 (previous step)

c ' + x + b ' = y + a ' + a ' + z ⊦ a = b, a ∈ x

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
c ' + x + b ' = y + a ' + a ' + z, c ∈ y ∨ c ∈ a ' ∨ c ∈ z ⊦ a = b, a ∈ x

Rule argument

Additional information

Used simplifier rules: in-16: ⊦ x + a ' = y + b ' + z ∧ a ≠ b → a ∈ z;%a: ⊦ (x + y) + z = x + y + z;%in-14: ⊦ a ' + x = y → a ∈ y;%in-15: ⊦ x + a ' = y → a ∈ y;%in-append: ⊦ a ∈ x + y ↔ a ∈ x ∨ a ∈ y;%in-16: ⊦ x + a ' = y + b ' + z ∧ a ≠ b → a ∈ z;