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Proof step 35 from proof reachable-addnew-rev (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 36:
path(r ' + x1 + r2 ' + x0, H[r2, ce]), r ∈ H, (r2 ' + x0).last ∈ H ⊦ r2 ∈ H, r ∈ x1, r ∈ x0, r2 ∈ x1, r2 ∈ x0, dups(x1 + x0), reachable(r, (r2 ' + x0).last, H), dups(x1), dups(x0), reachable(r, (r ' + x1).last, H) ∧ H[(r ' + x1).last].nxt = r2 ∧ H[(r ' + x1).last].nxt ≠ null ∧ reachable(ce.nxt, (H[(r ' + x1).last].nxt ' + x0).last, H)

Rule argument

Additional information

Used simplifier rules: c: ⊦ r + x0 = r ' + x0; from specification list[reflist]