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Proof step 18 from proof uni-ass (previous step)

r ∈ (H0 ∪ H1) ∪ H, r ∈ H0 ∪ H1 ∪ H, H0 ⊥ H1, H1 ⊥ H, H ⊥ H0, r ∈ H ∨ r ∈ H1 ⊦ (r ∈ H1 ⊃ H1[r];H[r]) = (H1 ∪ H)[r], r ∈ H0

Heuristic cut applied rule cut formula

And closed the goal!

Rule argument

fma: r ∈ H1

Additional information

Used simplifier rules: in-uni: ⊦ H0 ⊥ H1 → (r ∈ H0 ∪ H1 ↔ r ∈ H0 ∨ r ∈ H1);%at-uni: r ∈ H0 ∪ H1 ⊦ H0 ⊥ H1 → (H0 ∪ H1)[r] = (r ∈ H0 ⊃ H0[r];H1[r]);%in-uni: ⊦ H0 ⊥ H1 → (r ∈ H0 ∪ H1 ↔ r ∈ H0 ∨ r ∈ H1);%disj-r: ⊦ r ∈ H1 ∧ H0 ⊥ H1 → (r ∈ H0 ↔ false);%at-uni: r ∈ H0 ∪ H1 ⊦ H0 ⊥ H1 → (H0 ∪ H1)[r] = (r ∈ H0 ⊃ H0[r];H1[r]); Used formulas: r ∈ H1