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Proof step 5 from proof disj-write (previous step)

⊦ (∀ r0. ¬ r0 ∈ H0 ∨ ¬ r0 ∈ (H1 ++ r)[r, o]) ↔ H0 ⊥ H1 ∧ ¬ r ∈ H0, r = null, r ∈ H1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
∀ r0. ¬ r0 ∈ H0 ∨ r0 ≠ r ∧ ¬ r0 ∈ H1 ⊦ r = null, r ∈ H1, H0 ⊥ H1 ∧ ¬ r ∈ H0

Rule argument

Additional information

Used simplifier rules: in-write: ⊦ r ∈ H[r0, o] ↔ r ∈ H;%in-alloc: r0 ≠ null, ¬ r0 ∈ H ⊦ r ∈ H ++ r0 ↔ r = r0 ∨ r ∈ H;%disj-l: ⊦ r ∈ H0 ∧ H0 ⊥ H1 → (r ∈ H1 ↔ false);