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Proof step 1 from proof reachable-n-rec-strong (conclusion)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ reachable-n(H, n + 1, r, r0) ↔ (∃ r1. reachable-1(H, r, r1) ∧ reachable-n(H, n, r1, r0))
Proof step 3:
⊦ (∃ r1. reachable-1(H, r, r1) ∧ reachable-n(H, n, r1, r0)) ↔ reachable-1(H, r, H[r].nxt) ∧ reachable-n(H, n, H[r].nxt, r0)

Rule argument

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

Additional information

Used terms: r0, r, n, H