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Proof step 12 from proof rem-reachable-rev-weak (previous step)

ce.nxt = H[H[r1].nxt].nxt, r = r1, path(H[r1, ce][r].nxt ' + x0, H[r1, ce]), reachable(H[r1, ce][r].nxt, (H[r1, ce][r].nxt ' + x0).last, H), r1 ∈ H, H[r1].nxt ∈ H, r ∈ H[r1, ce] ⊦ (H[r1, ce][r].nxt ' + x0).last = H[r1].nxt, H[r1].nxt = null, r = 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 13:
ce.nxt = H[H[r1].nxt].nxt, path(ce.nxt ' + x0, H[r1, ce]), reachable(ce.nxt, (ce.nxt ' + x0).last, H), H[r1].nxt ∈ H, r1 ∈ H ⊦ (ce.nxt ' + x0).last = H[r1].nxt, H[r1].nxt = null, r1 = null, reachable(r1, (ce.nxt ' + x0).last, H)

Rule argument

Additional information

Used simplifier rules: ⊦ r ∈ H[r, ce]; (s)% ⊦ H[r, ce][r] = ce; (s)