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Proof step 63 from proof add-preserves-reachable-rev (previous step)

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