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Proof step 25 from proof reach-n-path-n (previous step)

reachable-1(H, H[r].nxt, r0), r ∈ H, H[r].nxt ∈ H, ∀ H0, r4, r5. reachable-1(H0, r4, r5) ↔ (∃ x. path(x, H0) ∧ hd x = r4 ∧ x.last = r5 ∧ # x = 2) ⊦ H[r].nxt = null, r = null, H[H[r].nxt].nxt ∈ H ∧ H[H[r].nxt].nxt ≠ null ∧ H[H[r].nxt].nxt = r0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 26:
⊦ reachable-1(H, r, r0) ↔ r ≠ null ∧ r0 ≠ null ∧ r ∈ H ∧ r0 ∈ H ∧ H[r].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, H[r].nxt, H] flags: rewrite, current

Additional information

Used terms: r0, H[r].nxt, H