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Proof step 28 from proof rem-stays-reachable-aux2 (previous step)

(r0 ' + x0).last = (r ' + x).last, ∃ x0. path(r ' + x0, H) ∧ (r ' + x0).last = (r ' + x).last ∧ ¬ dups(r ' + x0), path(r ' + x + H[r0].nxt ', H), reachable(r, r0, H), H[r0].nxt ∈ H, r0 ∈ H, path(r0 ' + x0, H), (r ' + x).last ∈ H ⊦ H[r0].nxt = null, r0 = r, r0 ∈ x, r0 ∈ x0, dups(x0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 29:
(r0 ' + x0).last = (r ' + x).last, (r ' + x1).last = (r ' + x).last, path(r ' + x1, H), path(r ' + x + H[r0].nxt ', H), reachable(r, r0, H), H[r0].nxt ∈ H, r0 ∈ H, path(r0 ' + x0, H), (r ' + x).last ∈ H ⊦ H[r0].nxt = null, r0 = r, r0 ∈ x, r0 ∈ x0, dups(x0), r ∈ x1, dups(x1)

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]