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Proof step 32 from proof rem-stays-reachable-aux2 (previous step)

(r0 ' + x0).last = (r ' + x).last, (r ' + x1).last = (r ' + x).last, path(r ' + x + H[r0].nxt ', H), path(r0 ' + x0, H), path(r ' + x1, H), (r ' + x).last ∈ H, r0 ∈ H, H[r0].nxt ∈ H, ∃ x. path(r ' + x, H) ∧ (r ' + x).last = r0 ∧ ¬ dups(r ' + x) ⊦ H[r0].nxt = null, r0 = r, dups(x1), dups(x0), r ∈ x1, r0 ∈ x0, r0 ∈ x

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 33:
(r ' + x1).last = (r ' + x).last, ((r ' + x2).last ' + x0).last = (r ' + x).last, path(r ' + x2, H), path(r ' + x1, H), path((r ' + x2).last ' + x0, H), path(r ' + x + H[(r ' + x2).last].nxt ', H), H[(r ' + x2).last].nxt ∈ H, (r ' + x2).last ∈ H, (r ' + x).last ∈ H ⊦ (r ' + x2).last = r, H[(r ' + x2).last].nxt = null, dups(x0), dups(x1), dups(x2), (r ' + x2).last ∈ x, (r ' + x2).last ∈ x0, r ∈ x1, r ∈ x2

Rule argument

Additional information

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