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Proof step 60 from proof add-preserves-reachable-rev (previous step)

reachable(H[r].nxt, ce.nxt, 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)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 61:
H[r1].nxt = H[ce.nxt].nxt, reachable(r, r1, H), reachable(H[r].nxt, ce.nxt, H), (H[r].nxt ' + x0).last ∈ H[r1, ce], r1 ∈ H, path(H[r].nxt ' + x0, H[r1, ce]), r ∈ H, ce.nxt ∈ H ⊦ r = null, (H[r].nxt ' + x0).last = ce.nxt, ce.nxt = null, r = r1, reachable(r, (H[r].nxt ' + x0).last, H), reachable(r, ce.nxt, H)

Rule argument

Additional information

Used simplifier rules: reach-alloc: ⊦ reachable(r, r1, H) → r1 ∈ H;%in-neq: ⊦ r ≠ r0 → (r ∈ H[r0, ce] ↔ r ∈ H); from specification store[linheap]