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Proof step 19 from proof diff-union (previous step)

¬ a ∈ z, ∀ z. rmdup(y0) \ z = rmdup(y0 \ z) ⊦ (a ' + rmdup(y0)) \ z = rmdup(a + (y0 \ z)), a ∈ y0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 20:
∀ z. rmdup(y0) \ z = rmdup(y0 \ z) ⊦ a ' + (rmdup(y0) \ z) = rmdup(a ' + (y0 \ z)), a ∈ y0, a ∈ z

Rule argument

Additional information

Used simplifier rules: diff-n: ⊦ ¬ a ∈ y → (a ' + x) \ y = a + (x \ y);%a: ⊦ (x + y) + z = x + y + z; from specification list%c: ⊦ a + x = a ' + x; from specification list