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Proof step 41 from proof rem-stays-reachable-aux1 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 42:
path(H[H[r].nxt].nxt ' + x1 + r ', H), path(H[H[r].nxt].nxt ' + x0 + H[r].nxt ', H), H[r].nxt ∈ H, r ∈ H ⊦ H[r].nxt = null, H[r].nxt = H[H[r].nxt].nxt, r = H[H[r].nxt].nxt, dups(x1), r ∈ x0, H[H[r].nxt].nxt ∈ x1, r ∈ x1

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)