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Proof step 21 from proof reachable-addnew-rev (previous step)

(r ' + x1).last ≠ r1, H[(r ' + x1).last].nxt = r1, r ∈ H, path(r ' + x1, H) ⊦ r1 = null, r1 ∈ H, r ∈ x1, r1 ∈ x1, dups(x1), reachable(r, (r ' + x1).last, H) ∧ H[(r ' + x1).last].nxt = r1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 22:
r ∈ H, path(r ' + x1, H) ⊦ H[(r ' + x1).last].nxt = null, (r ' + x1).last = H[(r ' + x1).last].nxt, H[(r ' + x1).last].nxt ∈ H, r ∈ x1, H[(r ' + x1).last].nxt ∈ x1, dups(x1), reachable(r, (r ' + x1).last, H)

Proof step 21 from proof reachable-addnew-rev (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information