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Proof step 36 from proof acyclic-rem-not-reachable (previous step)

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

User applied rule constructor cut

And obtained the following new goals

Proof step 37:
x1 = [], ce.nxt = H[H[r].nxt].nxt, r ∈ H, path(r ' + x1 + H[r].nxt ', H[r, ce]), H[r].nxt ∈ H, ∀ r1. ¬ reachable(H[r1].nxt, r1, H) ⊦ H[r].nxt = null, r = H[r].nxt, r = null, r ∈ x1, H[r].nxt ∈ x1, dups(x1)
Proof step 39:
x1 = r0 + x, ce.nxt = H[H[r].nxt].nxt, r ∈ H, path(r ' + x1 + H[r].nxt ', H[r, ce]), H[r].nxt ∈ H, ∀ r1. ¬ reachable(H[r1].nxt, r1, H) ⊦ H[r].nxt = null, r = H[r].nxt, r = null, r ∈ x1, H[r].nxt ∈ x1, dups(x1)

Rule argument

var: x1

Additional information

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