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Proof step 11 from proof reachable-addnew-rev (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
path(r ' + x, H[(r ' + x).last, ce]), r ∈ H ⊦ dups(x), (r ' + x).last ∈ H, r ∈ x, ∃ r0. reachable(r, r0, H) ∧ H[r0].nxt = (r ' + x).last ∧ H[r0].nxt ≠ null

Rule argument

Additional information

Used simplifier rules: a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]% ⊦ dups(r ' + x0) ↔ dups(x0) ∨ r ∈ x0; (ws)