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Proof step 3 from proof inapp-13 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
a ' + x = y + b ', a ∈ y, b ∈ x, c ∈ x ⊦ c = b, y = [], c ∈ y

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;