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Proof step 37 from proof rem-stays-reachable-aux2 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 38:
(r ' + x1).last = (r ' + x).last, (x2.last ' + x0).last = (r ' + x).last, x2 = x + H[x2.last].nxt ', path(r ' + x1, H), path(x2.last ' + x0, H), path(r ' + x2, H), H[x2.last].nxt ∈ H, x2.last ∈ H, (r ' + x).last ∈ H, H[x2.last].nxt ∈ x2 ⊦ x2.last = r, H[x2.last].nxt = null, dups(x0), dups(x1), dups(x2), x2.last ∈ x, x2.last ∈ x0, r ∈ x1, r ∈ x2

Rule argument

Additional information

Used simplifier rules: ⊦ r ∈ x0 → (r0 ' + x0).last = x0.last; (s)%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]%in-15: ⊦ x0 + r ' = x1 → r ∈ x1; (forward) from specification list[reflist]