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Proof step 31 from proof acyclic-rem-not-reachable (previous step)

¬ ¬ r0 ∈ r ' + x1 + H[r0].nxt ', 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)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 32:
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 = r ∨ r0 = H[r0].nxt ⊦ H[r0].nxt = null, r = H[r0].nxt, r0 ∈ x1, r ∈ x1, H[r0].nxt ∈ x1, dups(x1)

Rule argument

Additional information

Used simplifier rules: a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]%in-17: ⊦ r ∈ r0 ' ↔ r = r0; from specification list[reflist]%in-append: ⊦ r ∈ x0 + x1 ↔ ¬ ¬(r ∈ x0 ∨ r ∈ x1); from specification list[reflist]%in-rec: ⊦ r ∈ r0 ' + x0 ↔ ¬ ¬(r = r0 ∨ r ∈ x0); from specification list[reflist]