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Proof step 4 from proof rm-empty (previous step)

rmdup(a ' + x0) = [] ⊦ rmdup(x0) = [], x0 = []

Heuristic cut applied rule cut formula

And closed the goal!

Rule argument

fma: a ∈ x0

Additional information

Used simplifier rules: rmdup-y: ⊦ a ∈ x → rmdup(a ' + x) = rmdup(x);%rmdup-n: ⊦ ¬ a ∈ x → rmdup(a ' + x) = a + rmdup(x);% ⊦ a + x = a ' + x; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ x + y = [] ↔ x = [] ∧ y = []; (as)% ⊦ a ' ≠ []; (s) Used formulas: a ∈ x0