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Proof step 192 from proof rem-stays-reachable-aux2 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 193:
H[r0].nxt = H[r1].nxt, path(H[H[r1].nxt].nxt ' + x3 + r1 ', H), H[r1].nxt ∈ H, r0 ∈ H, path(r ' + x1 + r0 ', H), path(r ' + (x1 + r0 ') + H[r1].nxt ' + (H[H[r1].nxt].nxt ' + x3) + r1 ', H), r1 ∈ H, path(r1 ' + x + r0 ', H) ⊦ H[r1].nxt = null, r = H[H[r1].nxt].nxt, H[r1].nxt = H[H[r1].nxt].nxt, r1 = H[H[r1].nxt].nxt, r1 = r, r = H[r1].nxt, H[r1].nxt = r1, H[H[r1].nxt].nxt = r0, r1 = r0, r = r0, r ∈ x1, r ∈ x3, H[r1].nxt ∈ x1, dups(x1), dups(x3), H[r1].nxt ∈ x3, r1 ∈ x3, r0 ∈ x1, r0 ∈ x3, dups(x1 + x3), H[H[r1].nxt].nxt ∈ x1, H[H[r1].nxt].nxt ∈ x3, r1 ∈ x1, r1 ∈ x, r0 ∈ 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]