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Proof step 28 from proof reachable-addnew-rev (previous step)

∃ x. path(r ' + x, H[r2, ce]) ∧ (r ' + x).last = r1 ∧ ¬ dups(r ' + x), r ∈ H, r1 ∈ H ⊦ reachable(r, r1, H), r2 ∈ H, ∃ r0. reachable(r, r0, H) ∧ H[r0].nxt = r2 ∧ H[r0].nxt ≠ null ∧ reachable(ce.nxt, r1, H)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 29:
path(r ' + x, H[r2, ce]), r ∈ H, (r ' + x).last ∈ H ⊦ reachable(r, (r ' + x).last, H), r2 ∈ H, r ∈ x, dups(x), ∃ r0. reachable(r, r0, H) ∧ H[r0].nxt = r2 ∧ H[r0].nxt ≠ null ∧ reachable(ce.nxt, (r ' + x).last, H)

Rule argument

Additional information

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