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Proof step 17 from proof acyclic-rem-not-reachable (previous step)

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

User applied rule constructor cut

And obtained the following new goals

Proof step 18:
x = [], path(r0 ' + x + H[r0].nxt ', H[r0, ce]), ce.nxt = H[H[r0].nxt].nxt, r0 ∈ H, path(r ' + (x0 + r0 ' + x) + H[r0].nxt ', H[r0, ce]), reachable(r, r0, H), H[r0].nxt ∈ H, ∀ r1. ¬ reachable(H[r1].nxt, r1, H) ⊦ H[r0].nxt = null, r = H[r0].nxt, r = r0, H[r0].nxt = r0, r0 ∈ x, r ∈ x0, r ∈ x, H[r0].nxt ∈ x0, H[r0].nxt ∈ x, r0 ∈ x0, dups(x0 + x), dups(x0), dups(x)
Proof step 20:
x = r2 + x1, path(r0 ' + x + H[r0].nxt ', H[r0, ce]), ce.nxt = H[H[r0].nxt].nxt, r0 ∈ H, path(r ' + (x0 + r0 ' + x) + H[r0].nxt ', H[r0, ce]), reachable(r, r0, H), H[r0].nxt ∈ H, ∀ r1. ¬ reachable(H[r1].nxt, r1, H) ⊦ H[r0].nxt = null, r = H[r0].nxt, r = r0, H[r0].nxt = r0, r0 ∈ x, r ∈ x0, r ∈ x, H[r0].nxt ∈ x0, H[r0].nxt ∈ x, r0 ∈ x0, dups(x0 + x), dups(x0), dups(x)

Rule argument

var: x

Additional information

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