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Proof step 56 from proof rem-stays-reachable-aux1 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 57:
path(H[H[r].nxt].nxt ' + x0 + H[r].nxt ', H), H[r].nxt ∈ H, r ∈ H, path(H[H[r].nxt].nxt ' + x0 + H[r].nxt ' + r1 ' + x1 + r ', H) ⊦ r = H[r].nxt, r = H[H[r].nxt].nxt, H[r].nxt = null, H[r].nxt = H[H[r].nxt].nxt, H[H[r].nxt].nxt = r1, r = r1, H[r].nxt = r1, H[r].nxt ∈ x0, r ∈ x0, r1 ∈ x1, H[H[r].nxt].nxt ∈ x1, H[H[r].nxt].nxt ∈ x0, r ∈ x1, r1 ∈ x0, dups(x0 + x1), H[r].nxt ∈ x1, dups(x0), dups(x1)

Rule argument

Additional information

Used simplifier rules: a: ⊦ ¬ dups(x0 + x1) → ¬ dups(x0) ∧ ¬ dups(x1); (forward) from specification list-dup[reflist]%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]%e-02: ⊦ x0 + r ' ≠ []; from specification list[reflist]