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Proof step 59 from proof reachable-addnew-rev (previous step)

(ce.nxt ' + x).last ∈ H, r ∈ H, path(ce.nxt ' + x, H[H[r].nxt, ce]) ⊦ H[r].nxt = ce.nxt, r = null, r = H[r].nxt, H[r].nxt = null, reachable(r, (ce.nxt ' + x).last, H), dups(x), ce.nxt ∈ x, H[r].nxt ∈ x, r ∈ x, H[r].nxt ∈ H, path(ce.nxt ' + x, H), 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 [], +;;%c: ⊦ r + x0 = r ' + x0; from specification list[reflist]%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]%l-05: ⊦ (r ' + r0 ' + x0).last = (r0 ' + x0).last; from specification list-last[reflist]%in-neq: ⊦ r ≠ r0 → (r ∈ H[r0, ce] ↔ r ∈ H); from specification store[linheap]%app: ⊦ x0 + [] = x0; from specification list[reflist]%l: ⊦ r '.last = r; from specification list-last[reflist]