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Proof step 11 from proof diff-union (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
rmdup(y0) \ z = rmdup(y0 \ z), a ∈ y0 ⊦ rmdup(y0) \ z = rmdup(a ' + (y0 \ z)), a ∈ z

Rule argument

Additional information

Used simplifier rules: c: ⊦ a + x = a ' + x; from specification list