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Proof step 7 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 ⊦ modify(rs) ^*(H1, H0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ PHH ^*(H, H0) ↔ (∃ n. rtc(n, PHH)(H, H0))
Proof step 9:
¬ 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)

Rule argument

spec: rtc, inst: rtc-heap name: rtc seq: ⊦ PHH ^*(H, H0) ↔ (∃ n. rtc(n, PHH)(H, H0)) subst: [H0, H, PHH] → [H0, H1, modify(rs)] flags: <all paths>

Additional information

Used terms: H0, H1, modify(rs)