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Proof step 34 from proof reachable-addnew-rev (previous step)

path(r ' + x, H[r2, ce]), x.last ∈ H, r ∈ H, ∃ x1, x2. x = x1 + (r2 + x2) ⊦ dups(x), reachable(r, x.last, H), r ∈ x, r2 ∈ H, ∃ r0. reachable(r, r0, H) ∧ H[r0].nxt = r2 ∧ H[r0].nxt ≠ null ∧ reachable(ce.nxt, x.last, H)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 35:
path(r ' + x1 + r2 ' + x0, H[r2, ce]), r ∈ H, (r2 ' + x0).last ∈ H ⊦ dups(x1 + x0), dups(x1), dups(x0), reachable(r, (r2 ' + x0).last, H), r2 ∈ H, r ∈ x1, r ∈ x0, r2 ∈ x1, r2 ∈ x0, ∃ r0. reachable(r, r0, H) ∧ H[r0].nxt = r2 ∧ H[r0].nxt ≠ null ∧ reachable(ce.nxt, (H[r0].nxt ' + x0).last, H)

Rule argument

Additional information

Used simplifier rules: a: ⊦ ¬ dups(x0 + x1) → ¬ dups(x0) ∧ ¬ dups(x1); (forward) from specification list-dup[reflist]% ⊦ dups(x0 + r ' + x1) ↔ r ∈ x0 ∨ r ∈ x1 ∨ dups(x0 + x1); (ws)% ⊦ r ∈ r0 ' ↔ r = r0; (s)% ⊦ r ∈ x0 + x1 ↔ r ∈ x0 ∨ r ∈ x1; (s)% ⊦ (x0 + r ' + x1).last = (r ' + x1).last; (s)%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]% ⊦ r + x0 = r ' + x0; (s)