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Proof step 8 from proof reachable-n-rec-rev2 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ reachable-n(H, n + 1, r, r0) ↔ (∃ r1. reachable-n(H, n, r, r1) ∧ reachable-1(H, r1, r0))
Proof step 10:
reachable-1(H, r1, r0), reachable-n(H, n + 2, r, r0), reachable-n(H, (n + 1) + 1, r, r0), ∃ r2. reachable-n(H, n, r, r2) ∧ reachable-1(H, r2, r1) ⊦ ∃ r1. reachable-n(H, n, r, r1) ∧ reachable-1(H, r1, H[r1].nxt) ∧ reachable-1(H, H[r1].nxt, r0)

Rule argument

spec: <toplevel> 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] → [r1, r, n, H] flags: <all paths>

Additional information

Used terms: r1, r, n, H