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Proof step 6 from proof rm-rm-01 (previous step)

∀ y. rmdup(rmdup(x0) + y) = rmdup(x0 + y) ⊦ a ∈ x0, rmdup(rmdup(a ' + x0) + y) = rmdup((a ' + x0) + y)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
∀ y. rmdup(rmdup(x0) + y) = rmdup(x0 + y) ⊦ rmdup((a ' + rmdup(x0)) + y) = rmdup((a ' + x0) + y), a ∈ x0

Rule argument

Additional information

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