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Proof step 1 from proof reachable-n-rec2 (conclusion)

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

User applied rule insert 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:
reachable-n(H, 1 + 1, r, r0) ↔ (∃ r1. reachable-1(H, r, r1) ∧ reachable-n(H, 1, r1, r0)) ⊦ reachable-n(H, 2, r, r0) ↔ reachable-1(H, r, H[r].nxt) ∧ reachable-1(H, 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: [H, n, r, r0] → [H, 1, r, r0] flags: current, []

Additional information

Used terms: H, 1, r, r0