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Proof step 15 from proof reachable-nodups-def (previous step)

r ≠ H[r].nxt, (H[r].nxt ' + x).last = (H[r].nxt ' + x0).last, path(H[r].nxt ' + x0, H), r ∈ H, path(H[r].nxt ' + x, H), ∀ r, H. path(r ' + x0, H) → (∃ x1. path(r ' + x1, H) ∧ (r ' + x1).last = (r ' + x0).last ∧ ¬ r ∈ x1 ∧ ¬ dups(x1)) ⊦ r = null, dups(x), H[r].nxt ∈ x, ∃ x. path(r ' + x, H) ∧ (r ' + x).last = (H[r].nxt ' + x0).last ∧ ¬ r ∈ x ∧ ¬ dups(x), r ≠ H[r].nxt ∧ ¬ r ∈ x

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 16:
x.last = (H[r].nxt ' + x0).last, path(H[r].nxt ' + x0, H), r ∈ H, path(H[r].nxt ' + x, H), r ∈ x, ∀ r, H. path(r ' + x0, H) → (∃ x1. path(r ' + x1, H) ∧ (r ' + x1).last = (r ' + x0).last ∧ ¬ r ∈ x1 ∧ ¬ dups(x1)) ⊦ r = null, r = H[r].nxt, dups(x), H[r].nxt ∈ x, ∃ x. path(r ' + x, H) ∧ (r ' + x).last = (H[r].nxt ' + x0).last ∧ ¬ r ∈ x ∧ ¬ dups(x)

Rule argument

Additional information

Used simplifier rules: a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]%l-in: ⊦ r ∈ x0 → (r0 ' + x0).last = x0.last; from specification list-last[reflist]