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Proof step 12 from proof rem-stays-reachable-aux1 (previous step)

r = H[r0].nxt, x = x1 + r ', path(H[r].nxt ' + x, H), r ∈ H, r0 ∈ H ⊦ r = null, r = H[r].nxt, x = [], dups(x), reachable(H[r].nxt, r0, H), H[r].nxt ∈ x, ∃ x. path(H[r0].nxt ' + x + H[r0].nxt ', H) ∧ ¬ r0 ∈ x

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
path(H[H[r0].nxt].nxt ' + x1 + H[r0].nxt ', H), r0 ∈ H, H[r0].nxt ∈ H ⊦ H[r0].nxt = H[H[r0].nxt].nxt, H[r0].nxt = null, dups(x1), reachable(H[H[r0].nxt].nxt, r0, H), H[H[r0].nxt].nxt ∈ x1, H[r0].nxt ∈ x1, ∃ x. path(H[r0].nxt ' + x + H[r0].nxt ', H) ∧ ¬ r0 ∈ 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)