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Proof step 12 from proof acyclic-rem-not-reachable (previous step)

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

User applied rule cut formula

And obtained the following new goals

Proof step 13:
r0 ∈ x1, ce.nxt = H[H[r0].nxt].nxt, path(r ' + x1 + H[r0].nxt ', H[r0, ce]), reachable(r, r0, H), H[r0].nxt ∈ H, H[r0].nxt ∈ H[r0, ce], r0 ∈ H, ∀ r1. ¬ reachable(H[r1].nxt, r1, H) ⊦ H[r0].nxt = null, r = H[r0].nxt, r ∈ x1, H[r0].nxt ∈ x1, dups(x1)
Proof step 29:
ce.nxt = H[H[r0].nxt].nxt, path(r ' + x1 + H[r0].nxt ', H[r0, ce]), reachable(r, r0, H), H[r0].nxt ∈ H, H[r0].nxt ∈ H[r0, ce], r0 ∈ H, ∀ r1. ¬ reachable(H[r1].nxt, r1, H) ⊦ r0 ∈ x1, H[r0].nxt = null, r = H[r0].nxt, r ∈ x1, H[r0].nxt ∈ x1, dups(x1)

Rule argument

fma: r0 ∈ x1

Additional information

Used formulas: r0 ∈ x1