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Proof step 142 from proof rem-stays-reachable-aux2 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 143:
(r0 ' + x0).last = (r2 ' + x2.butlast).last, H[r0].nxt = x2.last, (r ' + x1).last = (r2 ' + x2.butlast).last, path(r0 ' + x0, H), r0 ∈ H, x2.last ∈ H, path(r ' + x1 + r2 ' + x2 + r0 ', H), path(r ' + x1 + r2 ' + x2, H), path(r ' + x1, H), (r2 ' + x2.butlast).last ∈ H ⊦ r2 = r0, r = r2, r0 = r, x2.last = null, x2 = [], dups(x2), dups(x1), dups(x1 + x2), r0 ∈ x2, r0 ∈ x1, r2 ∈ x2, r2 ∈ x1, r ∈ x2, r ∈ x1, dups(x0), r0 ∈ x0, r0 ∈ x2.butlast

Rule argument

Additional information

Used simplifier rules: lin-02: ⊦ x0.last = r ∧ x0 ≠ [] → r ∈ x0; from specification list-last[reflist]%in-01: ⊦ r ≠ r0 → (r ∈ r0 ' + x0 ↔ r ∈ x0); from specification list[reflist]%lapp-03: ⊦ (r ' + x0 + r0 ' + x1).last = (r0 ' + x1).last; from specification list-last[reflist]%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]%l-02: ⊦ x0 ≠ [] → (r ' + x0).last = x0.last; from specification list-last[reflist]