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Proof step 14 from proof rm-rm-01 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

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

Rule argument

Additional information

Used simplifier rules: rm-in-01: ⊦ a ∈ rmdup(x) → a ∈ x;%rm-in-05: ⊦ a ∈ x → rmdup(a ' + x + y) = rmdup(x + y);%rm-in-04: ⊦ a ∈ y → 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% ⊦ a ∈ x + y ↔ a ∈ x ∨ a ∈ y; (s)