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Proof step 145 from proof rem-stays-reachable-aux2 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 146:
(r0 ' + x0).last = (r2 ' + x).last, (r ' + x1).last = (r2 ' + x).last, path(r0 ' + x0, H), path(r ' + x1 + r2 ' + x + H[r0].nxt ', H), path(r ' + x1 + r2 ' + (x + H[r0].nxt ') + r0 ', H), path(r ' + x1, H), H[r0].nxt ∈ H, r0 ∈ H, (r2 ' + x).last ∈ H ⊦ H[r0].nxt = null, r = r2, r = H[r0].nxt, r0 = r, r0 = H[r0].nxt, r2 = r0, r2 = H[r0].nxt, dups(x0), dups(x1 + x), dups(x1), dups(x), r0 ∈ x0, r ∈ x1, r ∈ x, r0 ∈ x1, r2 ∈ x, r2 ∈ x1, r0 ∈ x, H[r0].nxt ∈ x, H[r0].nxt ∈ x1

Rule argument

Additional information

Used simplifier rules: a: ⊦ ¬ dups(x0 + x1) → ¬ dups(x0) ∧ ¬ dups(x1); (forward) from specification list-dup[reflist]% ⊦ dups(x0 + r ') ↔ r ∈ x0 ∨ dups(x0); (ws)% ⊦ r ∈ r0 ' ↔ r = r0; (s)% ⊦ r ∈ x0 + x1 ↔ r ∈ x0 ∨ r ∈ x1; (s)%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]% ⊦ x0 + r ' ≠ []; (s)