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Proof step 2 from proof reach-reachnext (previous step)

reachable(r, r1, H), r1 ∈ H ⊦ ¬ reachable(r, H[r1].nxt, H) ↔ H[r1].nxt = null ∨ ¬ H[r1].nxt ∈ 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(r ' + x, H) ∧ (r ' + x).last = r1, r1 ∈ H ⊦ ¬ reachable(r, H[r1].nxt, H) ↔ H[r1].nxt = null ∨ ¬ H[r1].nxt ∈ 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, r1, r] flags: rewrite, current

Additional information

Used terms: H, r1, r