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Proof step 62 from proof acyclic-rem-not-reachable (previous step)

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

User applied rule constructor cut

And obtained the following new goals

Proof step 63:
r1 ' + x = x0 + r0 ', ce.nxt = H[H[r0].nxt].nxt, x0 = [], path(r ' + x1 + H[r0].nxt ', H), path(r ' + (x1 + H[r0].nxt ' + x0) + r0 ', H), H[r0].nxt ∈ H, r0 ∈ H, ∀ r1. ¬ reachable(H[r1].nxt, r1, H), r0 = r1 ∨ r0 ∈ x, r1 ∈ x0 ∨ r1 = r0 ⊦ H[r0].nxt = null, r = H[r0].nxt, r0 = H[r0].nxt, r0 = r, dups(x0), dups(x1), dups(x1 + x0), H[r0].nxt ∈ x0, r0 ∈ x0, r ∈ x0, r0 ∈ x1, r ∈ x1, H[r0].nxt ∈ x1
Proof step 72:
r1 ' + x = x0 + r0 ', ce.nxt = H[H[r0].nxt].nxt, x0 = r2 + x2, path(r ' + x1 + H[r0].nxt ', H), path(r ' + (x1 + H[r0].nxt ' + x0) + r0 ', H), H[r0].nxt ∈ H, r0 ∈ H, ∀ r1. ¬ reachable(H[r1].nxt, r1, H), r0 = r1 ∨ r0 ∈ x, r1 ∈ x0 ∨ r1 = r0 ⊦ H[r0].nxt = null, r = H[r0].nxt, r0 = H[r0].nxt, r0 = r, dups(x0), dups(x1), dups(x1 + x0), H[r0].nxt ∈ x0, r0 ∈ x0, r ∈ x0, r0 ∈ x1, r ∈ x1, H[r0].nxt ∈ x1

Rule argument

var: x0

Additional information

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