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Proof step 48 from proof add-preserves-reachable-rev (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 49:
H[r1].nxt = H[ce.nxt].nxt, path(ce.nxt ' + x0, H[r1, ce]), (ce.nxt ' + x0).last ∈ H[r1, ce], r1 ∈ H, ce.nxt ∈ H ⊦ (ce.nxt ' + x0).last = ce.nxt, ce.nxt = null, r1 = null, reachable(r1, ce.nxt, H), reachable(r1, (ce.nxt ' + x0).last, H), H[r1].nxt ∈ H ∧ H[r1].nxt ≠ null

Rule argument

Additional information

Used simplifier rules: path-two: ⊦ path(r ' + r0 ', H) ↔ r ∈ H ∧ r0 ∈ H ∧ r ≠ null ∧ r0 ≠ null ∧ H[r].nxt = r0;% ⊦ (x0 + r ').last = r; (s)%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]