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Proof step 22 from proof rem-stays-reachable-aux (previous step)

¬ r ∈ ce.nxt ' + x2 + H[r].nxt ', ce.nxt = H[H[r].nxt].nxt, r ∈ H, path(ce.nxt ' + x2 + H[r].nxt ', H), H[r].nxt ∈ H ⊦ r = ce.nxt, r = null, H[r].nxt = null, H[r].nxt = ce.nxt, r = H[r].nxt, H[r].nxt ∈ x2, dups(x2), ce.nxt ∈ x2, r ∈ x2, ∃ x. path(H[r].nxt ' + x + H[r].nxt ', H) ∧ ¬ r ∈ x

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 23:
ce.nxt = H[H[r].nxt].nxt, r ∈ H, path(ce.nxt ' + x2 + H[r].nxt ', H), H[r].nxt ∈ H ⊦ r = ce.nxt, r = null, H[r].nxt = null, H[r].nxt = ce.nxt, r = H[r].nxt, H[r].nxt ∈ x2, dups(x2), ce.nxt ∈ x2, r ∈ x2, ∃ x. path(H[r].nxt ' + x + H[r].nxt ', H) ∧ ¬ r ∈ x

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-01: ⊦ r ≠ r0 → (r ∈ r0 ' + x0 ↔ r ∈ x0); from specification list[reflist]