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Proof step 156 from proof rem-stays-reachable-aux2 (previous step)

x1 + r2 ' + x2 = x + H[(r0 ' + y).last].nxt ' + r0 ' + y.butlast, ((r0 ' + y).last ' + x0).last = (r ' + x).last, (r ' + x1).last = (r ' + x).last, path((r0 ' + y).last ' + x0, H), path(r ' + x + H[(r0 ' + y).last].nxt ', H), path(r ' + x1 + r2 ' + x2 + (r0 ' + y).last ', H), path(r ' + x1, H), H[(r0 ' + y).last].nxt ∈ H, (r0 ' + y).last ∈ H, (r ' + x).last ∈ H, (r0 ' + y).last = H[(r0 ' + y).last].nxt ∨ (r0 ' + y).last = r0 ∨ (r0 ' + y).last ∈ y ⊦ (r0 ' + y).last = r, H[(r0 ' + y).last].nxt = null, r = r2, r2 = (r0 ' + y).last, y = [], dups(x2), dups(x1), dups(x1 + x2), dups(x0), (r0 ' + y).last ∈ x2, (r0 ' + y).last ∈ x1, r2 ∈ x2, r2 ∈ x1, (r0 ' + y).last ∈ x, (r0 ' + y).last ∈ x0, r ∈ x1, r ∈ x2

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 157:
x1 + r2 ' + x2 = x + H[y.last].nxt ' + r0 ' + y.butlast, (r ' + x1).last = (r ' + x).last, (y.last ' + x0).last = (r ' + x).last, path(r ' + x1, H), path(r ' + x1 + r2 ' + x2 + y.last ', H), path(r ' + x + H[y.last].nxt ', H), path(y.last ' + x0, H), (r ' + x).last ∈ H, y.last ∈ H, H[y.last].nxt ∈ H ⊦ y.last = r, H[y.last].nxt = null, r = r2, r2 = y.last, y = [], dups(x0), dups(x1 + x2), dups(x1), dups(x2), r ∈ x2, r ∈ x1, y.last ∈ x0, y.last ∈ x, r2 ∈ x1, r2 ∈ x2, y.last ∈ x1, y.last ∈ x2

Rule argument

Additional information

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