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Proof step 9 from proof reachable-trans (previous step)

(H[r].nxt ' + x0).last ∈ H, reachable((H[r].nxt ' + x0).last, r1, H), path(H[r].nxt ' + x0, H), r ∈ H, r1 ∈ H, reachable(H[r].nxt, r1, H) ⊦ r = null, reachable(r, r1, H)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

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

Additional information

Used simplifier rules: self-reachable: ⊦ reachable(r, r, H) ↔ ¬ ¬(r ≠ null ∧ r ∈ H);%reachable-notnullinH: ⊦ reachable(r, r1, H) → (¬ r1 ∈ H ↔ false); Used terms: H, r1, r