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Proof step 127 from proof rem-stays-reachable-aux2 (previous step)

x0 = x + r1 ', r1 = (r ' + x1).last, H[H[r0].nxt].nxt = r0, path(r ' + x1 + H[r0].nxt ', H), H[r0].nxt ∈ H, r0 ∈ H, path(r0 ' + x0, H), r1 ∈ H, path(r ' + x1, H) ⊦ H[r0].nxt = null, r0 = r, r = H[r0].nxt, H[r0].nxt = r0, r0 = null, x0 = [], dups(x1), r0 ∈ x0, dups(x0), r ∈ x1, H[r0].nxt ∈ x1, r0 ∈ x1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 128:
H[H[r0].nxt].nxt = r0, path(r ' + x1 + H[r0].nxt ', H), H[r0].nxt ∈ H, r0 ∈ H, path(r0 ' + x + (r ' + x1).last ', H), (r ' + x1).last ∈ H, path(r ' + x1, H) ⊦ H[r0].nxt = null, r0 = r, r = H[r0].nxt, H[r0].nxt = r0, r0 = null, r0 = (r ' + x1).last, r ∈ x1, H[r0].nxt ∈ x1, r0 ∈ x1, dups(x1), r0 ∈ x, (r ' + x1).last ∈ x, dups(x)

Rule argument

Additional information

Used simplifier rules: f: ⊦ dups(x0 + r ') ↔ r ∈ x0 ∨ dups(x0); from specification list-dup[reflist]%in-17: ⊦ r ∈ r0 ' ↔ r = r0; 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]%e-02: ⊦ x0 + r ' ≠ []; from specification list[reflist]