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Proof step 72 from proof rem-stays-reachable-aux2 (previous step)

x1 = x2, x2 = (x + H[x2.last].nxt ') + r0 ' + y, (x2.last ' + x0).last = (r ' + x).last, (r ' + x1).last = (r ' + x).last, path(r ' + x1, H), path(r ' + x + H[x2.last].nxt ', H), path(r ' + x2, H), H[x2.last].nxt ∈ H, x2.last ∈ H, path(x2.last ' + x0, H), (r ' + x).last ∈ H ⊦ H[x2.last].nxt = null, x2.last = r, x2 = [], x2.last ∈ x, x2.last ∈ x0, dups(x0), r ∈ x1, dups(x1), r ∈ x2, dups(x2)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 73:
x2 = (x + H[x2.last].nxt ') + r0 ' + y, (x2.last ' + x0).last = x2.last, x2.last = (r ' + x).last, path(r ' + x + H[x2.last].nxt ', H), path(r ' + x2, H), H[x2.last].nxt ∈ H, path(x2.last ' + x0, H), x2.last ∈ H ⊦ H[x2.last].nxt = null, x2.last = r, x2 = [], x2.last ∈ x, x2.last ∈ x0, dups(x0), r ∈ x2, dups(x2)

Rule argument

Additional information

Used simplifier rules: a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]%l-02: ⊦ x0 ≠ [] → (r ' + x0).last = x0.last; from specification list-last[reflist]