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Proof step 5 from proof rm-rm-02 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
∀ y. rmdup(x0 + rmdup(y)) = rmdup(x0 + y) ⊦ a ' + rmdup(x0 + rmdup(y)) = rmdup((a ' + x0) + y), a ∈ x0, a ∈ y

Rule argument

Additional information

Used simplifier rules: rmdup-n: ⊦ ¬ a ∈ x → rmdup(a ' + x) = a + rmdup(x);%rm-in-02: ⊦ a ∈ rmdup(x) ↔ a ∈ x;%in-append: ⊦ a ∈ x + y ↔ ¬ ¬(a ∈ x ∨ a ∈ y); from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list%c: ⊦ a + x = a ' + x; from specification list