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Proof step 2 from proof neq-02 (previous step)

c ' + z = y1 + a ' + x ⊦ a = c, a ∈ z

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
c ' + z = y1 + a ' + x, c ∈ y1 ⊦ a = c, a ∈ z

Rule argument

Additional information

Used simplifier rules: in-14: ⊦ a ' + x = y → a ∈ y;%a: ⊦ (x + y) + z = x + y + z;%in-append: ⊦ a ∈ x + y ↔ a ∈ x ∨ a ∈ y;%inapp-02: ⊦ ¬ a ∈ y → (y + c ' + z = a ' + z0 ↔ y = [] ∧ c = a ∧ z = z0);