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Proof step 70 from proof reachable-addnew-rev (previous step)

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