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Proof step 65 from proof rem-stays-reachable-aux (previous step)

ce.nxt = H[H[r].nxt].nxt, path(H[r].nxt ' + x1 + H[r].nxt ', H), r ∈ H, H[r].nxt ∈ H ⊦ H[r].nxt = null, H[r].nxt = ce.nxt, r = null, r ∈ x1, ∃ x. path(r ' + x, H[r, ce]) ∧ (r ' + x).last = H[r].nxt

User applied rule constructor cut

And obtained the following new goals

Proof step 66:
ce.nxt = H[H[r].nxt].nxt, x1 = r0 + x0, path(H[r].nxt ' + x1 + H[r].nxt ', H), H[r].nxt ∈ H, r ∈ H ⊦ H[r].nxt = ce.nxt, H[r].nxt = null, r = null, r ∈ x1, ∃ x. path(r ' + x, H[r, ce]) ∧ (r ' + x).last = H[r].nxt

Rule argument

var: x1

Additional information

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