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

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

User applied rule cut formula

And obtained the following new goals

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

Rule argument

fma: a ∈ rmdup(x)

Additional information

Used simplifier rules: ⊦ ¬ a ∈ x → x ≠ y + a ' + z; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list Used formulas: a ∈ rmdup(x)