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Proof step 202 from proof rem-stays-reachable-aux2 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 203:
x + H[x2.last].nxt ' = x2 + r1 ' + x3, (x2.last ' + x0).last = (r ' + x).last, (r ' + x1).last = (r ' + x).last, path(r ' + x1, H), path(r ' + x2 + r1 ' + x3, 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 ∈ x2 ∨ H[x2.last].nxt = r1 ∨ H[x2.last].nxt ∈ x3 ⊦ x2 = [], H[x2.last].nxt = null, x2.last = r, x2.last ∈ x, x2.last ∈ x0, dups(x0), r ∈ x1, dups(x1), r ∈ x2, dups(x2)

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]