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Proof step 2 from proof fromnext-reachable-rev (previous step)

reachable(H[r].nxt, r0, H), r ∈ H, r0 ∈ H ⊦ r = null, r = r0, reachable(r, r0, H)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ reachable(r, r0, H) ↔ (∃ x. path(r ' + x, H) ∧ (r ' + x).last = r0)
Proof step 4:
∃ x. path(H[r].nxt ' + x, H) ∧ (H[r].nxt ' + x).last = r0, r ∈ H, r0 ∈ H ⊦ r = null, r = r0, reachable(r, r0, H)

Rule argument

spec: inst: name: reachable-def seq: ⊦ reachable(r, r0, H) ↔ (∃ x. path(r ' + x, H) ∧ (r ' + x).last = r0) subst: [H, r0, r] → [H, r0, H[r].nxt] flags: rewrite, current

Additional information

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