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Proof step 28 from proof reachable-n-rec-rev2 (previous step)

reachable-n(H, n, r, r1), reachable-1(H, r1, H[r1].nxt), reachable-1(H, H[r1].nxt, r0) ⊦ reachable-n(H, (n + 1) + 1, r, r0), reachable-n(H, n + 2, r, r0), reachable-n(H, n + 1, r, H[r1].nxt)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 29:
⊦ reachable-n(H, n + 1, r, r0) ↔ (∃ r1. reachable-n(H, n, r, r1) ∧ reachable-1(H, r1, r0))
Proof step 30:
reachable-n(H, n, r, r1), reachable-1(H, r1, H[r1].nxt), reachable-1(H, H[r1].nxt, r0) ⊦ reachable-n(H, (n + 1) + 1, r, r0), reachable-n(H, n + 2, r, r0), ∃ r2. reachable-n(H, n, r, r2) ∧ reachable-1(H, r2, H[r1].nxt)

Rule argument

spec: inst: name: reachable-n-rec-rev seq: ⊦ reachable-n(H, n + 1, r, r0) ↔ (∃ r1. reachable-n(H, n, r, r1) ∧ reachable-1(H, r1, r0)) subst: [r0, r, n, H] → [H[r1].nxt, r, n, H] flags: rewrite, current

Additional information

Used terms: H[r1].nxt, r, n, H