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Proof step 1 from proof inapp-09 (conclusion)

⊦ x + y = z + a ' ∧ c ' + x = x0 + b ' ∧ x0 ≠ [] ∧ a ≠ b → b ∈ z

Heuristic simplifier applied rule simplifier

And closed the goal!

Rule argument

Additional information

Used simplifier rules: inapp-08: ⊦ a ' + x = y + b ' ∧ y ≠ [] → a ∈ y ∧ b ∈ x;%a: ⊦ (x + y) + z = x + y + z;%in-14: ⊦ a ' + x = y → a ∈ y;%in-15: ⊦ x + a ' = y → a ∈ y;%in-11: ⊦ a ∈ x → a ∈ x + y;%in-12: ⊦ a ∈ y → a ∈ x + y;%in-append: ⊦ a ∈ x + y ↔ ¬ ¬(a ∈ x ∨ a ∈ y);%inapp-13: ⊦ a ' + x = y + b ' ∧ c ∈ x ∧ c ≠ b → c ∈ y;%inapp-11: ⊦ x + y = z + a ' ∧ b ∈ x ∧ a ≠ b → b ∈ z;