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Proof step 12 from proof modify-agree (previous step)

rtc(n0 + 1, modify(rs))(H0, H1), ∀ rs, H0, H1. rtc(n0, modify(rs))(H0, H1) → ((H0 ≡ H1))(rs) ⊦ ((H0 ≡ H1))(rs)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ rtc(n + 1, PHH)(H, H0) ↔ (∃ H1. PHH(H, H1) ∧ rtc(n, PHH)(H1, H0))
Proof step 14:
∀ rs, H0, H1. rtc(n0, modify(rs))(H0, H1) → ((H0 ≡ H1))(rs), ∃ H2. modify(rs)(H0, H2) ∧ rtc(n0, modify(rs))(H2, H1) ⊦ ((H0 ≡ H1))(rs)

Rule argument

spec: rtc, inst: rtc-heap name: rtc-rec seq: ⊦ rtc(n + 1, PHH)(H, H0) ↔ (∃ H1. PHH(H, H1) ∧ rtc(n, PHH)(H1, H0)) subst: [H0, H, PHH, n] → [H1, H0, modify(rs), n0] flags: <all paths>

Additional information

Used terms: H1, H0, modify(rs), n0