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Proof step 9 from proof rm-rm-01 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
∀ y. rmdup(rmdup(x0) + y) = rmdup(x0 + y) ⊦ a ' + rmdup(rmdup(x0) + y) = rmdup((a ' + x0) + y), a ∈ rmdup(x0), a ∈ y, a ∈ x0

Rule argument

Additional information

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