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Proof step 19 from proof reachable-n-rec-rev2 (previous step)

reachable-n(H, (n + 1) + 1, r, r0), reachable-n(H, n, r, r2), reachable-1(H, r2, r1), reachable-1(H, r1, r0), reachable-n(H, n + 2, r, r0) ⊦ r2 ≠ null ∧ r2 ∈ H ∧ H[r2].nxt ≠ null ∧ H[H[r2].nxt].nxt ≠ null ∧ H[r2].nxt ∈ H ∧ H[H[r2].nxt].nxt ∈ H ∧ H[H[r2].nxt].nxt = r0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 20:
⊦ reachable-1(H, r, r0) ↔ r ≠ null ∧ r0 ≠ null ∧ r ∈ H ∧ r0 ∈ H ∧ H[r].nxt = r0
Proof step 21:
reachable-n(H, (n + 1) + 1, r, r0), reachable-n(H, n, r, r2), reachable-1(H, r2, r1), r1 ≠ null ∧ r0 ≠ null ∧ r1 ∈ H ∧ r0 ∈ H ∧ H[r1].nxt = r0, reachable-n(H, n + 2, r, r0) ⊦ r2 ≠ null ∧ r2 ∈ H ∧ H[r2].nxt ≠ null ∧ H[H[r2].nxt].nxt ≠ null ∧ H[r2].nxt ∈ H ∧ H[H[r2].nxt].nxt ∈ H ∧ H[H[r2].nxt].nxt = r0

Rule argument

spec: inst: name: reachable-1-def seq: ⊦ reachable-1(H, r, r0) ↔ r ≠ null ∧ r0 ≠ null ∧ r ∈ H ∧ r0 ∈ H ∧ H[r].nxt = r0 subst: [r0, r, H] → [r0, r1, H] flags: rewrite, current

Additional information

Used terms: r0, r1, H