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Proof step 3 from proof rm-notin-01 (previous step)

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

User applied rule case distinction

And obtained the following new goals

Proof step 4:
a ∈ rmdup(x), rmdup(x) = y + a ' + z ⊦ ¬ a ∈ y
Proof step 7:
a ∈ rmdup(x), rmdup(x) = y + a ' + z ⊦ ¬ a ∈ z

Rule argument

pos: right 1

Additional information

Used simplifier rules: rm-in-02: ⊦ a ∈ rmdup(x) ↔ a ∈ x;