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Proof step 2 from proof inapp-09 (previous step)

x + y = z + a ', c ' + x = x0 + b ' ⊦ a = b, x0 = [], b ∈ z

Heuristic simplifier applied rule simplifier

And closed the goal!

Rule argument

Additional information

Used simplifier rules: in-15: ⊦ x + a ' = y → a ∈ y;%a: ⊦ (x + y) + z = x + y + z;%inapp-08: ⊦ a ' + x = y + b ' ∧ y ≠ [] → a ∈ y ∧ b ∈ x;%in-14: ⊦ a ' + x = y → a ∈ y;%in-append: ⊦ a ∈ x + y ↔ a ∈ x ∨ a ∈ y;%in-17: ⊦ a ∈ b ' ↔ a = b;%inapp-11: ⊦ x + y = z + a ' ∧ b ∈ x ∧ a ≠ b → b ∈ z;%inapp-13: ⊦ a ' + x = y + b ' ∧ c ∈ x ∧ c ≠ b → c ∈ y;