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Proof step 12 from proof disj-write (previous step)

r ∈ H0, ∀ r0. ¬ r0 ∈ H0 ∨ r0 ≠ r ∧ ¬ r0 ∈ H1 ⊦ r = null, r ∈ H1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
r ∈ H0, ∀ r0. ¬ r0 ∈ H0 ∨ r0 ≠ r ∧ ¬ r0 ∈ H1 ⊦ r ∈ H1

Rule argument

Additional information

Used simplifier rules: nonnull: ⊦ r ∈ H → r ≠ null;