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Proof step 7 from proof sw-del-add-new (previous step)

r0 = r ⊦ r = null, r ∈ rs, r ∈ H, (r0 = r ∨ r0 ∈ H ∧ ¬ r0 ∈ rs → (r0 = r ∨ r0 ∈ H) ∧ ¬ r0 ∈ rs) ∧ ((r0 = r ∨ r0 ∈ H) ∧ ¬ r0 ∈ rs → ((H ++ r)[r, o] \ rs)[r0] = (r0 = r ⊃ o;((H \ rs) ++ r)[r0]))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
⊦ ((H ++ r)[r, o] \ rs)[r] = o, r = null, r ∈ H, r ∈ rs

Proof step 7 from proof sw-del-add-new (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information