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Proof step 50 from proof rem-stays-reachable-aux2 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 51:
H[r].nxt = H[H[r].nxt].nxt, path(H[r].nxt ' + x + r ', H), H[r].nxt ∈ H, r ∈ H ⊦ H[r].nxt = r, H[r].nxt = null, r = null, dups(x), H[r].nxt ∈ x, r ∈ x

Rule argument

Additional information

Used simplifier rules: ⊦ 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)