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Proof step 61 from proof acyclic-rem-not-reachable (previous step)

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

User applied rule constructor cut

And obtained the following new goals

Proof step 62:
x0 = [], ce.nxt = H[H[r0].nxt].nxt, r1 ' + x = x0 + r0 ', r0 ∈ H, path(r ' + x1 + H[r0].nxt ', H), path(r ' + (x1 + H[r0].nxt ' + x0) + r0 ', H), H[r0].nxt ∈ H, r1 ∈ x0 ∨ r1 = r0, ∀ r1. ¬ reachable(H[r1].nxt, r1, H), r0 = r1 ∨ r0 ∈ x ⊦ H[r0].nxt = null, r = H[r0].nxt, r0 = r, r0 = H[r0].nxt, r0 ∈ x1, r ∈ x1, H[r0].nxt ∈ x1, r ∈ x0, r0 ∈ x0, H[r0].nxt ∈ x0, dups(x1 + x0), dups(x1), dups(x0)
Proof step 71:
x0 = r2 + x2, ce.nxt = H[H[r0].nxt].nxt, r1 ' + x = x0 + r0 ', r0 ∈ H, path(r ' + x1 + H[r0].nxt ', H), path(r ' + (x1 + H[r0].nxt ' + x0) + r0 ', H), H[r0].nxt ∈ H, r1 ∈ x0 ∨ r1 = r0, ∀ r1. ¬ reachable(H[r1].nxt, r1, H), r0 = r1 ∨ r0 ∈ x ⊦ H[r0].nxt = null, r = H[r0].nxt, r0 = r, r0 = H[r0].nxt, r0 ∈ x1, r ∈ x1, H[r0].nxt ∈ x1, r ∈ x0, r0 ∈ x0, H[r0].nxt ∈ x0, dups(x1 + x0), dups(x1), dups(x0)

Rule argument

var: x0

Additional information

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