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Proof step 5 from proof uni-com (previous step)

H0 ⊥ H1 ⊦ ∀ r. (r ∈ H1 ∪ H0 ↔ r ∈ H0 ∪ H1) ∧ (r ∈ H1 ∪ H0 → (H1 ∪ H0)[r] = (H0 ∪ H1)[r])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
H0 ⊥ H1 ⊦ (r ∈ H1 ∪ H0 ↔ r ∈ H0 ∨ r ∈ H1) ∧ (r ∈ H1 ∪ H0 → (H1 ∪ H0)[r] = (H0 ∪ H1)[r])

Rule argument

Additional information

Used simplifier rules: in-uni: ⊦ H0 ⊥ H1 → (r ∈ H0 ∪ H1 ↔ r ∈ H0 ∨ r ∈ H1);