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Proof step 73 from proof rem-stays-reachable-aux2 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 74:
(x2.last ' + x0).last = x2.last, x2.last = (r ' + x).last, x2 = (x + H[x2.last].nxt ') + r0 ' + y, path(r ' + x + H[x2.last].nxt ', H), path(x2.last ' + x0, H), path(r ' + x2, H), x2.last ∈ H, H[x2.last].nxt ∈ H ⊦ x2.last = r, H[x2.last].nxt = null, x2 = [], dups(x2), dups(x0), r ∈ x2, x2.last ∈ x0, x2.last ∈ x

Rule argument

Additional information

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