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Proof step 199 from proof rem-stays-reachable-aux2 (previous step)

x + H[(r ' + x2).last].nxt ' = x2 + r1 ' + x3, ((r ' + x2).last ' + x0).last = (r ' + x).last, (r ' + x1).last = (r ' + x).last, path(r ' + x1, H), path(r ' + x + H[(r ' + x2).last].nxt ', H), path(r ' + x2, H), H[(r ' + x2).last].nxt ∈ H, (r ' + x2).last ∈ H, path((r ' + x2).last ' + x0, H), (r ' + x).last ∈ H ⊦ H[(r ' + x2).last].nxt = null, (r ' + x2).last = r, (r ' + x2).last ∈ x, (r ' + 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 200:
(r ' + x1).last = (r ' + x).last, ((r ' + x2).last ' + x0).last = (r ' + x).last, x + H[(r ' + x2).last].nxt ' = x2 + r1 ' + x3, (r ' + x).last ∈ H, path((r ' + x2).last ' + x0, H), (r ' + x2).last ∈ H, H[(r ' + x2).last].nxt ∈ H, path(r ' + x2, H), path(r ' + x2 + r1 ' + x3, H), path(r ' + x1, H), H[(r ' + x2).last].nxt ∈ x2 ∨ H[(r ' + x2).last].nxt = r1 ∨ H[(r ' + x2).last].nxt ∈ x3 ⊦ (r ' + x2).last = r, H[(r ' + x2).last].nxt = null, dups(x2), r ∈ x2, dups(x1), r ∈ x1, dups(x0), (r ' + x2).last ∈ x0, (r ' + x2).last ∈ x

Rule argument

Additional information

Used simplifier rules: in-rec: ⊦ r ∈ r0 ' + x0 ↔ ¬ ¬(r = r0 ∨ r ∈ x0); from specification list[reflist]%in-append: ⊦ r ∈ x0 + x1 ↔ ¬ ¬(r ∈ x0 ∨ r ∈ x1); from specification list[reflist]%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]%in-15: ⊦ x0 + r ' = x1 → r ∈ x1; (forward) from specification list[reflist]