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Proof step 18 from proof rem-reachable-rev-weak (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 19:
ce.nxt = H[H[r1].nxt].nxt, reachable(H[r].nxt, (H[r].nxt ' + x0).last, H), (H[r].nxt ' + x0).last ∈ H[r1, ce], r1 ∈ H, H[r1].nxt ∈ H, path(H[r].nxt ' + x0, H[r1, ce]), r ∈ H, (H[r].nxt ' + x0).last ∈ H ⊦ r = null, (H[r].nxt ' + x0).last = H[r1].nxt, H[r1].nxt = null, r1 = null, r = r1, reachable(r, (H[r].nxt ' + x0).last, 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]