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Proof step 4 from proof rm-notin-01 (previous step)

rmdup(x) = y + a ' + z, a ∈ rmdup(x) ⊦ a ∈ x ∧ ¬ a ∈ y ∧ ¬ a ∈ z

User applied rule case distinction

And obtained the following new goals

Proof step 5:
rmdup(x) = y + a ' + z, a ∈ rmdup(x) ⊦ a ∈ x
Proof step 7:
rmdup(x) = y + a ' + z, a ∈ y, a ∈ rmdup(x) ⊦
Proof step 10:
rmdup(x) = y + a ' + z, a ∈ z, a ∈ rmdup(x) ⊦

Rule argument

pos: right 1

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