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Proof step 1 from proof reachable-n-rec-strong2 (conclusion)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

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

Rule argument

Additional information

Used simplifier rules: reachable-n-rec: ⊦ reachable-n(H, n + 1, r, r0) ↔ (∃ r1. reachable-1(H, r, r1) ∧ reachable-n(H, n, r1, r0));%c: ⊦ m + n = n + m; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2