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Proof step 2 from proof rec (previous step)

⊦ dups(a ' + x) ↔ a ∈ x ∨ dups(x)

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 3:
a ∈ x ⊦ dups(a ' + x) ↔ a ∈ x ∨ dups(x)
Proof step 11:
⊦ a ∈ x, dups(a ' + x) ↔ a ∈ x ∨ dups(x)

Rule argument

fma: a ∈ x

Additional information

Used formulas: a ∈ x