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Proof step 71 from proof reachable-addnew-rev (previous step)

path(ce.nxt ' + x1, H[H[r0].nxt, ce]), path(r ' + x + r0 ' + H[r0].nxt ' + ce.nxt ' + x1, H[H[r0].nxt, ce]), path(r ' + x + r0 ', H), r0 ∈ H, (ce.nxt ' + x1).last ∈ H, r ∈ H ⊦ H[r0].nxt = ce.nxt, H[r0].nxt = null, r = r0, r0 = null, r0 = H[r0].nxt, dups(x1), dups(x), dups(x + x1), reachable(r, (ce.nxt ' + x1).last, H), ce.nxt ∈ x1, ce.nxt ∈ x, r0 ∈ x1, r0 ∈ x, H[r0].nxt ∈ x1, H[r0].nxt ∈ x, r ∈ x1, r ∈ x, H[r0].nxt ∈ H, ce.nxt ∈ H

User applied rule constructor cut

And closed the goal!

Rule argument

var: x1

Additional information

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