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Proof step 14 from proof rm-rm-02 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
a ∈ x0, ∀ y. rmdup(x0 + rmdup(y)) = rmdup(x0 + y) ⊦ rmdup(x0 + rmdup(y)) = rmdup(x0 + y), a ∈ rmdup(y), a ∈ y

Rule argument

Additional information

Used simplifier rules: rm-in-05: ⊦ a ∈ x → rmdup(a ' + x + y) = rmdup(x + y);%rm-in-03: ⊦ ¬ a ∈ rmdup(x) → ¬ a ∈ x;%a: ⊦ (x + y) + z = x + y + z; from specification list