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Proof step 9 from proof modify-sym (previous step)

¬ r ∈ rs ∧ r ≠ null ∧ ¬ r ∈ H0 ∧ H1 = H0 ++ r ∨ ¬ r0 ∈ rs ∧ r0 ∈ H0 ∧ H1 = H0[r0, o] ∨ ¬ r1 ∈ rs ∧ r1 ∈ H0 ∧ H1 = H0 -- r1 ⊦ ∃ n. rtc(n, modify(rs))(H1, H0)

User applied rule case distinction

And obtained the following new goals

Rule argument

pos: left 1

Additional information