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Proof step 188 from proof rem-stays-reachable-aux2 (previous step)

(r1 ' + x0).last = r0, H[r0].nxt = H[r1].nxt, x = x1 + r0 ', path(r ' + x, H), path(r ' + x + H[r1].nxt ' + (H[H[r1].nxt].nxt ' + x3) + r1 ', H), path(r1 ' + x0, H), path(H[H[r1].nxt].nxt ' + x3 + r1 ', H), H[r1].nxt ∈ H, r0 ∈ H, r1 ∈ H ⊦ H[r1].nxt = null, H[r1].nxt = H[H[r1].nxt].nxt, H[r1].nxt = r1, r = H[H[r1].nxt].nxt, r = H[r1].nxt, r1 = H[H[r1].nxt].nxt, r1 = r, x = [], dups(x3), dups(x), dups(x + x3), dups(x0), H[H[r1].nxt].nxt ∈ x, H[H[r1].nxt].nxt ∈ x3, r ∈ x3, r ∈ x, r1 ∈ x0, r1 ∈ x, H[r1].nxt ∈ x, H[r1].nxt ∈ x3, r1 ∈ x3

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 189:
H[(r1 ' + x0).last].nxt = H[r1].nxt, path(H[H[r1].nxt].nxt ' + x3 + r1 ', H), path(r1 ' + x0, H), path(r ' + (x1 + (r1 ' + x0).last ') + H[r1].nxt ' + (H[H[r1].nxt].nxt ' + x3) + r1 ', H), path(r ' + x1 + (r1 ' + x0).last ', H), r1 ∈ H, (r1 ' + x0).last ∈ H, H[r1].nxt ∈ H ⊦ H[r1].nxt = r1, H[r1].nxt = H[H[r1].nxt].nxt, H[r1].nxt = null, H[r1].nxt = (r1 ' + x0).last, H[H[r1].nxt].nxt = (r1 ' + x0).last, r = H[r1].nxt, r = H[H[r1].nxt].nxt, r = (r1 ' + x0).last, r1 = r, r1 = H[H[r1].nxt].nxt, r1 = (r1 ' + x0).last, dups(x0), dups(x1 + x3), dups(x1), dups(x3), r1 ∈ x3, H[r1].nxt ∈ x3, H[r1].nxt ∈ x1, r1 ∈ x1, r1 ∈ x0, r ∈ x1, r ∈ x3, H[H[r1].nxt].nxt ∈ x3, H[H[r1].nxt].nxt ∈ x1, (r1 ' + x0).last ∈ x1, (r1 ' + x0).last ∈ x3

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)% ⊦ dups(x0 + r ' + x1) ↔ r ∈ x0 ∨ r ∈ x1 ∨ dups(x0 + x1); (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)