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Proof step 27 from proof add-preserves-reachable (previous step)

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

Additional information

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