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Proof step 4 from proof in-uni (previous step)

H0 ⊥ H1, ∀ H, H0, r. # H < # H1 → H0 ⊥ H → (r ∈ H0 ∪ H ↔ r ∈ H0 ∨ r ∈ H) ⊦ r ∈ H0 ∪ H1 ↔ r ∈ H0 ∨ r ∈ H1

User applied rule cut formula

And obtained the following new goals

Proof step 5:
H0 ⊥ H1, ∀ H, H0, r. # H < # H1 → H0 ⊥ H → (r ∈ H0 ∪ H ↔ r ∈ H0 ∨ r ∈ H) ⊦ r ∈ H0 ∪ H1 ↔ r ∈ H0 ∨ r ∈ H1, H1 = ∅

Rule argument

fma: H1 = ∅

Additional information

Used simplifier rules: uni-emp-r: ⊦ H ∪ ∅ = H;%in-emp: ⊦ ¬ r ∈ ∅; Used formulas: H1 = ∅