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Proof step 8 from proof rem-reachable-rev-weak (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
ce.nxt = H[H[r1].nxt].nxt, (H[r1, ce][r].nxt ' + x0).last ∈ H[r1, ce], r1 ∈ H, H[r1].nxt ∈ H, path(H[r1, ce][r].nxt ' + x0, H[r1, ce]), r ∈ H[r1, ce], reachable(H[r1, ce][r].nxt, (H[r1, ce][r].nxt ' + x0).last, H), (H[r1, ce][r].nxt ' + x0).last ∈ H ⊦ r = null, (H[r1, ce][r].nxt ' + x0).last = H[r1].nxt, H[r1].nxt = null, r1 = null, reachable(r, (H[r1, ce][r].nxt ' + x0).last, H)

Rule argument

Additional information

Used simplifier rules: reach-alloc: ⊦ reachable(r, r1, H) → r1 ∈ H;