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Proof step 41 from proof diff-union (previous step)

¬(a ∈ x0 ∨ a ∈ y), ∀ y0, z0. rmdup(x0 + y0) \ z0 = rmdup((x0 \ z0) + (y0 \ z0)) ⊦ (a ' + rmdup(x0 + y)) \ z = rmdup((a ' + (x0 \ z)) + (y \ z)), a ∈ z

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 42:
∀ y0, z0. rmdup(x0 + y0) \ z0 = rmdup((x0 \ z0) + (y0 \ z0)) ⊦ a ' + (rmdup(x0 + y) \ z) = rmdup((a ' + (x0 \ z)) + (y \ z)), a ∈ z, a ∈ x0, a ∈ y

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