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Proof step 60 from proof reachable-addnew-rev (previous step)

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

User applied rule constructor cut

And closed the goal!

Rule argument

var: x

Additional information

Used simplifier rules: 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 ' + r0 ' + x0).last = (r0 ' + x0).last; (s)% ⊦ r ∈ H[r0, ce] ↔ r = r0 ∨ r ∈ H; (ws)% ⊦ x0 + [] = x0; (s)% ⊦ r '.last = r; (s)