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Proof step 65 from proof add-preserves-reachable-rev (previous step)

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

Additional information

Used simplifier rules: reach-alloc: ⊦ reachable(r, r1, H) → r1 ∈ H;%self-reachable: ⊦ reachable(r, r, H) ↔ ¬ ¬(r ≠ null ∧ r ∈ H);%reachable-notnullinH: ⊦ reachable(r, r1, H) → (¬ r1 ∈ H ↔ false);%In-insert: ⊦ r ∈ H[r0, ce] ↔ r = r0 ∨ r ∈ H; from specification store[linheap] Used terms: H, (H[r].nxt ' + x0).last, r