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Proof step 6 from proof sub-one (previous step)

∀ a0. a0 ∈ s → a0 = a ⊦ # s = 0, s = ∅ ++ a, s = ∅

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 7:
∀ a0. a0 ∈ s → a0 = a ⊦ # s = 0, s = ∅, s = ∅ ++ a, a ∈ ∅

Rule argument

fma: a ∈ ∅

Additional information

Used simplifier rules: eq: ⊦ a ∈ s → s ++ a = s;%In-empty: ⊦ ¬ a ∈ ∅; Used formulas: a ∈ ∅