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Proof step 7 from proof le (previous step)

# y < # filter(a ' + rmdup(x0), y), ∀ y. # y < # filter(rmdup(x0), y) → filter(rmdup(x0), y) = [] ⊦ filter(a ' + rmdup(x0), y) = [], a ∈ x0

Heuristic cut applied rule cut formula

And obtained the following new goals

Proof step 8:
a ∈ y, # y < # filter(a ' + rmdup(x0), y), ∀ y. # y < # filter(rmdup(x0), y) → filter(rmdup(x0), y) = [] ⊦ filter(a ' + rmdup(x0), y) = [], a ∈ x0
Proof step 10:
# y < # filter(a ' + rmdup(x0), y), ∀ y. # y < # filter(rmdup(x0), y) → filter(rmdup(x0), y) = [] ⊦ a ∈ y, filter(a ' + rmdup(x0), y) = [], a ∈ x0

Rule argument

fma: a ∈ y

Additional information

Used formulas: a ∈ y