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Proof step 32 from proof rem-stays-reachable-aux (previous step)

ce.nxt = H[r1].nxt, r1 = H[r0].nxt, x0 = x2 + r1 ', path(r ' + x1 + r0 ', H), path(r ' + x0, H[r0, ce]), r1 ∈ H[r0, ce], r0 ∈ H, r1 ∈ H ⊦ r = r1, r = r0, r1 = null, r1 = ce.nxt, x0 = [], dups(x1), dups(x0), r0 ∈ x1, r ∈ x0, r ∈ x1, ∃ x. path(r ' + x + r1 ', H) ∧ ¬ r0 ∈ x, ∃ x0. path(H[r0].nxt ' + x0 + H[r0].nxt ', H) ∧ ¬ r0 ∈ x0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 33:
ce.nxt = H[H[r0].nxt].nxt, path(r ' + x2 + H[r0].nxt ', H[r0, ce]), path(r ' + x1 + r0 ', H), H[r0].nxt ∈ H, r0 ∈ H, H[r0].nxt ∈ H[r0, ce] ⊦ H[r0].nxt = ce.nxt, H[r0].nxt = null, r = r0, r = H[r0].nxt, dups(x1), dups(x2), r ∈ x1, r ∈ x2, r0 ∈ x1, H[r0].nxt ∈ x2, ∃ x0. path(H[r0].nxt ' + x0 + H[r0].nxt ', H) ∧ ¬ r0 ∈ x0, ∃ x. path(r ' + 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)