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Proof step 37 from proof acyclic-rem-not-reachable (previous step)

ce.nxt = H[H[r].nxt].nxt, path(r ' + x1 + H[r].nxt ', H[r, ce]), r ∈ H, H[r].nxt ∈ H, ∀ r1. ¬ reachable(H[r1].nxt, r1, H) ⊦ H[r].nxt = null, r = H[r].nxt, r = null, dups(x1), H[r].nxt ∈ x1, r ∈ x1

User applied rule constructor cut

And obtained the following new goals

Proof step 38:
ce.nxt = H[H[r].nxt].nxt, x1 = [], path(r ' + x1 + H[r].nxt ', H[r, ce]), H[r].nxt ∈ H, r ∈ H, ∀ r1. ¬ reachable(H[r1].nxt, r1, H) ⊦ H[r].nxt = null, r = null, r = H[r].nxt, dups(x1), r ∈ x1, H[r].nxt ∈ x1
Proof step 40:
ce.nxt = H[H[r].nxt].nxt, x1 = r0 + x, path(r ' + x1 + H[r].nxt ', H[r, ce]), H[r].nxt ∈ H, r ∈ H, ∀ r1. ¬ reachable(H[r1].nxt, r1, H) ⊦ H[r].nxt = null, r = null, r = H[r].nxt, dups(x1), r ∈ x1, H[r].nxt ∈ x1

Rule argument

var: x1

Additional information

Used simplifier rules: reflist freely generated by [], +;;