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Proof step 152 from proof rem-stays-reachable-aux2 (previous step)

x = x2 + r1 ', (r0 ' + x0).last = r1, (r ' + x1).last = r1, path(r0 ' + x0, H), r0 ∈ H, H[r0].nxt ∈ H, path(r ' + x1 + r2 ' + (x + H[r0].nxt ') + r0 ', H), path(r ' + x1 + r2 ' + x + H[r0].nxt ', H), path(r ' + x1, H), r1 ∈ H ⊦ r2 = r0, r = r2, r0 = r, H[r0].nxt = null, r0 = H[r0].nxt, r2 = H[r0].nxt, r = H[r0].nxt, x = [], r ∈ x1, dups(x0), r0 ∈ x0, r0 ∈ x, H[r0].nxt ∈ x, H[r0].nxt ∈ x1, dups(x1 + x), r0 ∈ x1, r2 ∈ x, r2 ∈ x1, r ∈ x, dups(x1), dups(x)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 153:
(r ' + x1).last = (r0 ' + x0).last, path(r0 ' + x0, H), r0 ∈ H, H[r0].nxt ∈ H, path(r ' + x1 + r2 ' + ((x2 + (r0 ' + x0).last ') + H[r0].nxt ') + r0 ', H), path(r ' + x1 + r2 ' + (x2 + (r0 ' + x0).last ') + H[r0].nxt ', H), path(r ' + x1, H), (r0 ' + x0).last ∈ H ⊦ r2 = r0, r = r2, r0 = r, H[r0].nxt = null, r0 = H[r0].nxt, r2 = H[r0].nxt, r = H[r0].nxt, r0 = (r0 ' + x0).last, H[r0].nxt = (r0 ' + x0).last, r2 = (r0 ' + x0).last, r = (r0 ' + x0).last, r ∈ x1, dups(x0), r0 ∈ x0, r0 ∈ x2, H[r0].nxt ∈ x2, H[r0].nxt ∈ x1, (r0 ' + x0).last ∈ x1, (r0 ' + x0).last ∈ x2, dups(x1 + x2), r0 ∈ x1, r2 ∈ x2, r2 ∈ x1, r ∈ x2, dups(x1), dups(x2)

Rule argument

Additional information

Used simplifier rules: a: ⊦ ¬ dups(x0 + x1) → ¬ dups(x0) ∧ ¬ dups(x1); (forward) from specification list-dup[reflist]%l-03: ⊦ ¬ r ∈ x0 → (dups(x0 + r ') ↔ dups(x0)); from specification list-dup[reflist]%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]